As Democratic presidential candidates point the finger at the president's divisive rhetoric, Mulvaney said on ABC's "This Week" that the suspect who allegedly killed 20 people at a Walmart in El Paso appeared to have been motivated by beliefs he harbored before Trump became president.
Rep. Beto O'Rourke, a Texas Democrat running for president, on Saturday called Trump a "racist" and said he "stokes racism in this country." Fellow candidate Pete Buttigieg, the mayor of South Bend, Indiana, said Trump was "condoning white nationalism."
Several of those killed in El Paso, which borders Mexico, were Mexican citizens, and officials said that they are examining what they called a "manifesto" that they believe was written by the shooter and shows a possible "nexus" to a hate crime. After he was arrested, the suspect told investigators he wanted to shoot as many Mexicans as possible, two law enforcement officials told ABC News.
Marcelo Ebrard, Mexico's foreign minister, said six Mexicans were killed and nine were injured and that the nation is considering legal action against whomever provided the shooter with the assault weapon.
Pressed by Karl on whether Trump was at all to blame for using words like "invasion" to talk about illegal immigration and saying congresswomen of color should leave the country, Mulvaney said Trump was just as saddened and angered by the shootings as others.
"There's no benefit here to trying to make this a political issue," said Mulvaney. "This is a social issue."
He labeled the gunmen in El Paso and Dayton "crazy people" who "should not be able to get guns." The Dayton gunman, who died at the scene, killed at least nine people, authorities said. Dozens were injured in each attack.
"Sick people who are intent on doing things like this should not be able to buy guns legally," Mulvaney said.
Rep. Veronica Escobar, whose congressional district includes El Paso, said Saturday night that while investigators must complete an investigation, the El Paso suspect's so-called "manifesto" suggested the shooting could have been an act of "domestic terrorism."
“In this country, we have a gun violence epidemic but we also have a hate epidemic," Escobar said in an earlier interview on "This Week." "And until we confront that hate and until we confront the weak gun laws that we have we're going to keep seeing this.”
"Today's shooting in El Paso, Texas, was not only tragic, it was an act of cowardice," President Donald Trump tweeted overnight. "I know that I stand with everyone in this Country to condemn today's hateful act. There are no reasons or excuses that will ever justify killing innocent people."
After the Ohio attack, he tweeted that "Information is rapidly being accumulated in Dayton" and noted the law enforcement response "was very rapid in both" Dayton and El Paso. "God bless the people of El Paso Texas," he added. "God bless the people of Dayton, Ohio."
In March, ABC News Senior National Correspondent Terry Moran asked the president in the Oval Office if he thought white nationalism was a rising threat around the world.
Trump replied: "I don't really. I think it's a small group of people that have a very, very serious problem."
Pushed by Karl about why the president has downplayed the threat of white nationalism, Mulvaney said white nationalism is not as big a threat as "international nuclear weapons."
"I don't believe he's downplaying it. … Look, this is not the same as international, sort of, nuclear weapons," Mulvaney said. "This is a serious problem, there's no question about it. But they are sick, sick people. And the president knows that. Again, Jon, I don't think it's fair to try and lay this at the feet of the president."
"I don't think it's at all fair to sit here and say that he doesn't think that white nationalism is bad for the nation," Mulvaney added. "These are sick people. You cannot be a white supremacist and be normal in the head."
Later on "This Week," Julian Castro, a former secretary of housing and urban development who is running for the Democratic nomination for president, said said the shooter in El Paso bore responsibility, but added that "most presidents have chosen to try to bring people together."
"Anybody who has the ability to see and hear and understand what the president has been doing since he started his campaign in 2015 knows that division and bigotry and fanning the flames of hate has been his political strategy," Castro said. "He's given license for this toxic brew of white supremacy to fester more and more in this country. And we're seeing the results of that."
Washington Gov. Jay Inslee, another 2020 Democratic candidate, issued a statement late Sunday that read, in part:
"Donald Trump said today that 'hate has no place in our country,' but he has openly fostered and preached hate from his place in the White House. I stand by my statement from last week: We can no longer allow a white nationalist in the White House. He has been fanning the flames of racial disparity and hatred for years. America deserves a leader who will work to heal us rather than widen our divides. ... President Trump’s claim that he has 'done a lot' on gun violence prevention is a boldfaced lie."
ABC News' Josh Hoyos and John Verhovek contributed to this report.