New Jersey officials have contacted more than 200 people who attended a campaign fundraiser at the Trump National Golf Course in Bedminster hours before the president announced he had COVID-19.
Somerset County officials are meanwhile contacting employees who worked the event, most of whom live in the county.
In a joint statement issued on Sunday, the officials asked guests and employees to monitor for symptoms and, if they were close to President Trump or his staff, to quarantine for 14 days.
The officials, who started seeking the information on Friday, said on Sunday the White House had sent them a list of 206 guests.
They declined to say when they received the names. They were advising guests not to be tested for five to seven days out from the event.
"While the risk is low, a negative test earlier than that time cannot definitively rule out that COVID-19 will not develop," they said.
White House spokesman Judd Deere said the president had no contact with donors or staff that "would be considered to be 'close' based on CDC guidelines (more than 15 minutes and within two metres)."
"During the roundtable event and remarks, the President was more than 6 feet away from all participants," he said.
Dallas businessman Daniel Hux, who attended the event, said he felt fine on Sunday and had just undergone another test, as he and other donors had before the fundraiser.
"I'm grateful our president engaged his supporters safely while at the event," Hux said in a statement.
"My prayers are with our president and the first lady."
Hux, who owns a mortgage company, declined to say where he had traveled in the interim. He said he was never within two metres of the president but was quarantining just in case.
Dr Rich Roberts, a pharmaceutical executive from New Jersey who made a video describing the event, said he sat a seat away from Trump during an indoor roundtable event, which he said involved about 19 people and lasted perhaps 45 minutes or more.
Roberts did not return messages on Sunday about the video, which was posted on a local news site, The Lakewood (New Jersey) Scoop.
Charlie Kolean, also from Dallas, said the coronavirus test he took upon returning home from New Jersey came back negative on Sunday. He'll take another one in a few days.
Kolean, who works in investments, said from what he noticed, Trump campaign members were all masked and socially distant, as were Bedminster staff, who also wore gloves.
During the photo opportunity with the president, the 25-year-old said donors were required to stand two metres from the president, on a marker taped to the floor.
"I know there were rumors of him being lethargic or tired. That was not the case at all at this event. He was very high energy, happy to be there. I noticed no difference in his health from previous times," Kolean said.