The president, who is counting on support from military members and their families, suggested for the second time in a week that they might have spread the coronavirus at the White House.
WASHINGTON — Even as he scrambles to shore up support from his base, President Trump on Thursday again suggested that veterans and their families had spread the coronavirus at the White House, floating the idea that a meeting with the loved ones of fallen military members might have been the source of his own infection.
In an interview on Fox Business, Mr. Trump described an event at the White House on Sept. 27 with a group of Gold Star families — those whose relatives have died in military conflicts — and said he had “figured there would be a chance” he would become infected there, because the family members “come within an inch of my face sometimes.”
“They want to hug me and they want to kiss me,” he added. “And they do. And frankly, I’m not telling them to back up. I’m not doing it. But I did say it’s obviously dangerous.”
Last week, Mr. Trump suggested that Marines and other service members, as well as police officers, might have infected one of his top advisers, Hope Hicks. In fact, by the time the president made those comments, in an interview with Fox News on Thursday night, he had already tested positive using a rapid test and was awaiting the results of a more precise test.
The remarks came weeks after a report in The Atlantic that Mr. Trump — whose relationship with military leaders and prominent veterans has been a complex political brew of admiration and disdain — had disparaged American troops who died in wars as “losers” and “suckers.”
Mr. Trump has counted on veterans as well as active-duty service members as a key slice of his political base; in 2016, about 60 percent voted for him, according to exit polls, and swing-state counties with especially high numbers of veterans helped him win. But that support appears to have slipped.
Moreover, a large group of Republican former national security officials, including several retired generals, have thrown their support behind the president’s Democratic opponent, Joseph R. Biden Jr., as have a large number of former cabinet officials from both Bush administrations; Cindy McCain, the widow of Senator John McCain, Republican of Arizona; and many other prominent veterans.
The decline in military support, which mirrors that among other voters once loyal to the president, stems from a variety of factors, including increasing disenchantment with his attempts to insert the armed forces into his domestic political battles.
Groups associated with veterans and disillusioned Republican voters have raised millions of dollars to attack Mr. Trump since the Atlantic report early last month, which cited anonymous people who said the president had rejected a visit to a World War I military cemetery in northern France in part because it was “filled with losers.”
The group VoteVets alone raised $3.3 million in the last quarter, $1.5 million of it in September after it released an online ad critical of Mr. Trump that featured the parents of troops slain in Iraq and Afghanistan.
The president’s remarks on Thursday drew rebukes from liberal veterans and their political groups, as well as from elected Democrats, including the usually circumspect Senator Jack Reed, Democrat of Rhode Island, the ranking member of the Senate Armed Services Committee. “Whether he intended it or not, the president has blamed an event with families who lost their loved ones in battle for giving him Covid,” he said in a statement.
Mr. Reed added: “Instead of casting aspersions on the families of the fallen for infecting him, President Trump should be transparent about his own actions, who he met with and when, and release detailed medical information including a timeline and do some real contact tracing to help stop the spread. Instead, President Trump is continuing his pattern of irresponsible behavior.”
Alyssa Farah, a White House spokeswoman, said Mr. Trump had not been implicating the families. “His point was merely that in the time frame that he was potentially exposed,” she said, “there were a number of different venues he’d been at and individuals that he had interacted with that it could have come from.”
Many senior Pentagon leaders attended the event for military families late last month, and several guests there have since tested positive for the coronavirus, including Adm. Charles Ray, the vice commandant of the Coast Guard. The first lady, Melania Trump, was there and has also tested positive. Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, and several other senior uniformed leaders at the Pentagon are quarantining after interacting with Admiral Ray.
Scrutiny has also surrounded a White House gathering on Sept. 26, a day before the military event, which was held to honor Mr. Trump’s nomination of Judge Amy Coney Barrett to the Supreme Court. Numerous Trump aides and several Republican senators who were there have since tested positive, and the White House has done little to track the contacts of attendees.
In an email on Thursday, Timothy Davis, the president of the Greatest Generations Foundation, a veterans organization involved in organizing the Gold Star event on Sept. 27, said that all attendees had tested negative beforehand and that all were “doing well and exhibit no symptoms of Covid-19.” Mr. Davis said the group had been told late on Oct. 1 that Mr. Trump had tested positive, and the families in attendance were notified the next morning.
Tests, especially the rapid tests used by the White House for screening staff members and visitors, are not always accurate. For months, experts have emphasized the need to combine testing with other disease containment strategies, like mask-wearing and physical distancing.
Maggie Haberman contributed reporting.