Mr Trump's campaign manager reportedly tested positive for Covid-19 on Friday evening. Bill Stepien was said to be experiencing "mild flu-like symptoms", according to Politico.
Also on Friday, former White House counsellor Kellyanne Conway and Republican Senators Mike Lee and Thom Tillis announced they had tested positive.
All three attended Mr Trump's unveiling of his Supreme Court nominee, Judge Amy Coney Barrett, at the White House Rose Garden last Saturday.
Judge Coney Barrett tested positive for coronavirus earlier this year but has since recovered, unnamed officials told US media.
Republican National Committee Chairwoman Ronna McDaniel, who was with Mr Trump a week ago, has also tested positive, the party said on Friday.
On Thursday night, the first couple said they intended to self-isolate after one of Mr Trump's closest aides, Hope Hicks, tested positive. Soon afterwards, they too received positive test results.
There has been criticism of the president's decision to go to a fundraiser attended by dozens of people in New Jersey on Thursday, apparently when officials already knew about Ms Hicks' symptoms.