Asked at an afternoon Rose Garden news conference what message he had for those flouting restrictions, Trump replied, "Be safe," saying nothing more, declining to criticize them.
Trump also continued to threaten to Gov. Roy Cooper of North Carolina, a Democrat, that if he doesn't guarantee "within a week" that restrictions in the state will be lifted by August, the Republican National Committee might move its 2020 convention to another state.
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Here are Tuesday's most significant developments in Washington:
Trump denies mocking Biden for wearing mask, but then questions it as 'very unusual'
President Trump said that a retweet of his Monday appearing to belittle Democratic presidential nominee Joe Biden for wearing a mask was not actually meant to criticize Biden -- but then he questioned why Biden wore one.
"Biden can wear a mask, but he was standing outside with his wife, perfect conditions. Perfect weather. They are inside, they don't wear masks and so I thought it was very unusual that he had one on. But I thought that was fine. I wasn't criticizing him at all. Why would I do a thing like that?" the president said.
Trump made the remark at a White House event announcing a cap on copays for insulin for senior citizens.
"Sleepy Joe can't do this, that I can tell you," Trump said during his introductory remarks at a Rose Garden. "I hope the seniors are going to remember it."
The move comes as headlines note slipping support for the president among seniors in Florida -- a demographic that could prove key to his re-election.
His comments came just a few hours after his senior adviser Kellyanne Conway denied any political motivation, telling reporters, "We're talking prescription drugs today not politics here at the White House," when asked whether there was a political motivation for the announcement's timing amid those headlines.
Biden, meanwhile, responded to that retweet in an interview with CNN Tuesday by saying Trump was a "fool" and that experts all recommend wearing a mask.
ABC News' Ben Gittleson
McEnany reiterates Trump's charge that NC governor could use COVID-19 as political excuse to hamper GOP convention
White House press secretary Kayleigh McEnany referred questions this morning on decision-making surrounding the president's threats to pull the GOP convention from North Carolina to the RNC and campaign but suggests that the state's Democratic governor could use the coronavirus as a political excuse to restrict the event.
"The president wants to ensure that politics is not at play and determining how and when the convention can work," she said. "He wants to make sure a Democrat governor is not putting in place extraneous restrictions that would prohibit him from having the convention and holding it."
Gov. Roy Cooper has been following federal guidelines in responding to the virus in his state, which saw its highest one-day spike in cases over the weekend.
-- ABC News' Jordyn Phelps
HHS deputy inspector general, attacked by Trump, testifies on hospital shortages
After weathering criticism from President Trump in reaction to an early April over a Department of Health and Human Services report that detailed hospitals' concerns about equipment shortages, HHS Principal Deputy Inspector General Christi Grimm faced the House Oversight Committee today via video. Despite the controversy around Trump's attacks against Grimm, no Democratic lawmakers took the opportunity to ask her to react to it.
Grimm seemed ready to defend the importance of maintaining independence for inspectors general, but never mentioned President Trump by name or his dismissing her as a partisan.
"I do think that independence is the cornerstone of what any office of inspector general does. And that allows us to be impartial in the work that we do, and to go right down the middle and providing facts and letting the facts take us where we may," Grimm told Rep. Jackie Speier, D-Calif.
Grimm defended the early-April report repeatedly as a "snapshot in time," a way to gather "quick and reliable data," she said, about challenges hospitals were facing to share with administration officials and lawmakers alike. To compile the report, Grimm's office called a random sample of 400 hospitals across the country and received responses from 85% -- 323 hospitals. Interviews were conducted between March 23 and 27.
The report revealed hospitals had major concerns about having enough supplies like masks and ventilators, as well as toilet paper, linens, food, disinfectant, and healthy staff to oversee it all. At the time, it appeared to be the first publicly-available comprehensive survey detailing what hospitals were telling the federal government.
--ABC News' Sarah Kolinovsky and Anne Flaherty
WHO pauses trial of hydroxychloroquine, drug touted by Tump
The World Health Organization has temporarily halted its global trial of hydroxychloroquine, an antimalarial drug promoted by President Trump, due to safety concerns.
WHO director general said in a Monday briefing the "temporary pause" is in effect as safety data is being reviewed, while Trump pointed to its "tremendous, rave reviews" one day earlier.
"I believe in it enough that I took a program because I had two people in the White House that tested positive," Trump told Sinclair Broadcast Group's Sharyl Attkisson.
Trump said he finished a "two-week course" of the drug himself, paired with zinc, after weeks of promoting it at coronavirus task force briefings and on Twitter as a potential treatment for COVID-19.
Trump retweets snide comment on Biden wearing mask
The president on Monday retweeted Fox News analyst Brit Hume's comment on Democratic presidential candidate Joe Biden wearing a mask at a Memorial Day event in Delaware.
"This might help explain why Trump doesn't like to wear a mask in public. Biden today," the comment read, above an image of the former vice president.
The president was not seen with a face mask during his public Memorial Day appearances as he continues to resist wearing one in public.
White House proclamation on Brazil travel ban takes effect Tuesday night
A travel ban on foreign travelers arriving in the U.S. from Brazil will now take effect at 11:59 tonight, two days earlier than originally planned.
The White House issued a revision to the proclamation late Monday but did not provide an explanation.
"This proclamation is effective at 11:59 p.m. eastern daylight time on May 26, 2020. This proclamation does not apply to persons aboard a flight scheduled to arrive in the United States that departed prior to 11:59 p.m. eastern daylight time on May 26, 2020," it read.
-- ABC News' Jordyn Phelps