He got his family history wrong in a speech that also drew a link between wind power and cancer that has not been proved.
A look at some of the statements from a week of political rhetoric:
TRUMP, on why he is pulling back on sealing the U.S.-Mexico border: "Because Mexico has been absolutely terrific for the last four days. They're apprehending everybody. Yesterday they apprehended 1,400 people. The day before was 1,000. And if they apprehend people at their southern border where they don't have to walk through, that's a big home run. We can handle it from there. It's really good." — remarks to reporters Friday.
TRUMP: "Before that they never did anything." — remarks to reporters Thursday.
THE FACTS: Trump is describing a Mexican crackdown on Central American migrants that has not materialized. He's also wrong in saying that Mexico did nothing about the problem until he threatened to close the border.
Mexico markedly tightened migration controls during the Obama administration. Mexico also detained more than 30,000 foreigners in the first three months of this year, before Trump accused Mexican officials of doing "NOTHING."
Mexico reports that its interception and detention of migrants from the south are "about average" in recent months. Over the first three days of April, it apprehended 1,259 foreigners — not 1,000 or more a day, as Trump claimed.
"There is no very substantive change," said Mexico's foreign secretary, Marcelo Ebrard. "I don't know what (Trump) was referring to."
Ebrard said: "What Mexico is doing as far as the review of the southern border — well, it's the same thing it has been doing."
TRUMP: "The Flores decision is a disaster, I have to tell you. Judge Flores, whoever you may be, that decision is a disaster for our country, a disaster." — remarks at a meeting with local officials in Southern California on Friday.
THE FACTS: There's no Judge Flores involved. Jenny Flores was 15-year-old native of El Salvador who was held in what her advocates said were substandard conditions in the 1980s, contending she was strip-searched in custody and housed with male adults. They launched a class-action lawsuit on behalf of migrant children in the country illegally. Her mother was a housekeeper in the U.S. who feared deportation if she picked up her daughter.
The case worked its way to the Supreme Court, which sided with the government and against the girl's advocates. But the case gave rise to an agreement in 1997 setting conditions for the detention of migrant children and the codifying of those conditions in law a decade later. It generally bars the government from keeping children in immigration detention for more than 20 days and guides how they are to be treated.
TRUMP: "This will be a great campaign issue. I never asked Mitch McConnell for a vote before the Election as has been incorrectly reported (as usual) in the @nytimes, but only after the Election when we take back the House etc." — tweet Wednesday.
THE FACTS: That's misleading at best.
A week earlier, Trump stirred expectations of an ambitious health care effort when he said that if the Supreme Court strikes down "Obamacare," ''we will have a plan that's far better." He promised "the Republican Party will become the party of great health care."
But Trump soon found that the party in Congress had no appetite for yet another attempt to replace President Barack Obama's health law in the near future — nor does it have a plan.
"I made it clear to him that we were not going to be doing that in the Senate," Senate Majority Leader Mitch McConnell, R-Ky., told reporters Tuesday, describing their conversation a day earlier. "He did say, as he later tweeted, that he accepted that and that he would be developing a plan that he would take to the American people during the 2020 campaign."
So Trump backed down and postponed any replacement until after an election more than 18 months away.
McConnell explained to Trump that senators are open to tackling specific aspects of health care — namely, trying to lower prescription drug prices, according to a person who spoke on condition of anonymity to discuss Monday's private call between the two. But Trump's promised big, new health care bill wasn't going happen with Democrats running the House.
Trump told McConnell he "accepted" the situation and "would be developing a plan that he would take to the American people during the 2020 campaign," according to that person. That night, Trump tweeted as much.
TRUMP: "Republicans will always support pre-existing conditions!" — tweet Wednesday.
MICK MULVANEY, acting White House chief of staff: "Every single plan that this White House has ever put forward since Donald Trump was elected covered pre-existing conditions. Every single plan that Republicans in the House voted on in the previous Congress covered pre-existing conditions. Every single plan considered by the Senate covers pre-existing conditions. The debate about pre-existing conditions is over. Both parties support them and anyone telling you anything different is lying to you for political gain." — interview March 31 on ABC's "This Week."
THE FACTS: Trump and his chief of staff's sweeping statements about the GOP commitment to protect people with pre-existing medical conditions are misleading. The Republican health insurance proposals would not have protected those patients as broadly as the Obama-era law and could have led to significantly higher rates or gaps in coverage for people with chronic illnesses.
The Obama health law requires insurers to take all applicants, regardless of medical history, and patients with health problems pay the same standard premiums as healthy ones. It also requires standard benefits such as pregnancy, maternity and newborn care and mental health treatment. The trade-off was that the law also mandated that everyone have insurance, including healthy people, whose premiums helped insurers cover the costs of the very sick.
The GOP health overhaul plans in Congress eliminated the mandate that everyone have insurance and sought to protect people with pre-existing conditions to a degree. But the Republican legislation would have given states leeway to vary the premiums that insurers charge based on health and other factors. That might make coverage unaffordable for people with serious or pre-existing health conditions.
For instance, the Republican plans would have allowed insurers to charge older people at a 5-to-1 ratio compared with young people, higher than the law's 3-to-1 ratio, and given states authority to allow insurers to use health status as a factor in setting premiums for people who have had a break in coverage and are trying to get a new individual policy.
The nonpartisan Congressional Budget Office found the GOP plans over time would raise premiums for people with health problems because healthy people would be more likely to take their chances going uninsured.
TRUMP: "If you have a windmill anywhere near your house, congratulations. Your house just went down 75% of value. And they say the noise causes cancer." — remarks at Republican fundraising dinner Tuesday.
THE FACTS: The sound from wind farms has not been proved to cause cancer.
Trump has had it out for wind power since turbines were proposed off the coast of Scotland within sight of his golf resort near Aberdeen . He unsuccessfully fought the project. He has ascribed a variety of evils to wind power over the years, usually with scant evidence, while praising coal, a well-documented cause of health problems.
"The American Cancer Society is unaware of any credible evidence linking the noise from windmills to cancer," the organization said after Trump's latest remarks.
While some recesses of the internet have long tried to sound alarms about "wind turbine syndrome," several studies have found no evidence of serious health issues.
Trump actually misidentified his target. Wind turbines produce energy. Windmills mill grain and flummox Don Quixote .
TRUMP: "Puerto Rico got 91 Billion Dollars for the hurricane, more money than has ever been gotten for a hurricane before." — tweet Tuesday.
HOGAN GIDLEY, White House spokesman: "The fact is, they have received more money than any state or territory in history for a rebuild." — interview Tuesday with MSNBC.
THE FACTS: The money Puerto Rico has received for hurricane relief is nowhere close to $91 billion. Nor is the amount provided greater than for any other hurricane that has struck the U.S.
According to the White House, Trump's $91 billion estimate includes about $50 billion in expected future disaster disbursements that could span decades, along with $41 billion already approved. But actual aid to Puerto Rico has flowed more slowly from federal coffers, about $11 billion so far.
Even if the $91 billion figure eventually comes to fruition, it would not be the most ever provided for hurricane rebuilding efforts. Hurricane Katrina, which hit Louisiana and other Gulf Coast states in 2005, has cost the U.S government more than $120 billion.
TRUMP, on Puerto Rico: "The pols are grossly incompetent, spend the money foolishly or corruptly, & only take from USA." — tweet Tuesday.
THE FACTS: Trump appears to suggest Puerto Rico is not part of the U.S. as he criticizes its territorial government for taking "from USA." He does not criticize other Americans for taking "from USA."
Gidley, speaking on MSNBC, called the notion that Trump was referring to Puerto Ricans as noncitizens "absolutely ridiculous." But in the same interview Gidley had referred to Puerto Rico as "that country." When pressed about his wording, Gidley said it was a mistake and he meant to say "territory."
Puerto Ricans are Americans.
TRUMP, arguing that Germany should spend more on its own military budget: "I have great respect for Angela, and I have great respect for the country," he said, referring to German Chancellor Angela Merkel. "My father is German, right, was German, and born in a very wonderful place in Germany, and so I have a great feeling for Germany, but they're not paying what they should be paying." — remarks Tuesday with NATO's secretary general.
THE FACTS: Trump is confusing his father and grandfather.
Trump's father, Fred, was born in New York City. The president's grandfather, Friedrich, was born in Germany.
Friedrich Trump immigrated to the U.S. in 1885 at the age of 16, arriving in New York before moving to the western parts of the U.S.
Trump has messed up his family history in this way several times. Last year, he said both his parents were born in what became the European Union. Only his Scottish mother was.
DEMOCRAT BETO O'ROURKE: "The state saw young voter turnout up 500% over the last midterm election." — various campaign events in recent weeks.
THE FACTS: Voter turnout by people under 30 did not jump nearly that much last year. Texas did see a large increase in those young voters, though.
More than 1 million young voters cast a ballot in the 2018 midterm election, a 234% increase from the 2014 midterm elections, according to voting data from the Texas secretary of state's office.
Initial reports suggested young voter turnout increased as much as 508% during early voting in Texas when compared with early voting in 2014, according to data released by a political consulting firm a week before the 2018 election.
O'Rourke spokesman Chris Evans acknowledged his candidate used those figures without making the distinction that they represent an incomplete portion of early votes cast — not total turnout in the election.
Overall, voter turnout in the 2018 midterm election increased 77% in Texas over 2014 totals.
TRUMP: "Can you believe that the Radical Left Democrats want to do our new and very important Census Report without the all important Citizenship Question. Report would be meaningless and a waste of the $Billions (ridiculous) that it costs to put together!" — tweet Monday.
THE FACTS: Trump's disdain for conducting the once-a-decade census without a citizenship question is not shared by his own Census Bureau researchers. Nor is it consistent with the many operations of government and business that make billions of dollars in spending decisions as well as policy decisions based on the most accurate possible count of the U.S. population.
According to January 2018 calculations by the Census Bureau, adding a citizenship question to the decennial census form would cause lower response rates among noncitizens, leading to an increased cost to the government of at least $27.5 million for additional phone calls, visits to the home and other follow-up efforts to reach them. The Constitution requires a count every 10 years of "the whole number of persons in each state," long understood to include all residents of the U.S.
The count goes to the heart of the U.S. political system. It's used to determine the number of seats each state has in the House and how the electoral votes that decide presidential elections are distributed. Civil rights groups and states with higher shares of immigrant populations such as California and New York cite a significant harm to the political rights of minority groups if a citizenship question in the decennial census dissuades immigrants from participating, resulting in diminished representation in the U.S. House.
The census also shapes how 300 federal programs distribute more than $800 billion a year to local communities, according to an analysis by the GW Institute of Public Policy at George Washington University. Communities and businesses depend on it, as well, in deciding where to build schools, hospitals, job training centers, grocery stores and more.
The GW institute's analysis of the effects of an undercount on five programs administered by the Health and Human Services Department, for instance, found that 37 states lost a median of $1,091 in the 2015 budget year for each person missed in the 2010 census.
Associated Press writers Ricardo Alonso-Zaldivar, Michael Biesecker, Jill Colvin, Andrew Taylor and Alan Fram in Washington, Amanda Seitz in Chicago, Will Weissert in Austin, Texas, and Mark Stevenson in Mexico City contributed to this report.
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EDITOR'S NOTE _ A look at the veracity of claims by political figures