Trump, 73, and Vice President Mike Pence, 60, were being tested weekly for the coronavirus, according to CNN.
Trump told reporters on Thursday that the testing schedule would be increased to daily.
He said, "I’ve had very little contact with this person [who tested positive]."
In March, concern that the president and members of his administration would contract the virus grew in some circles after a number of government officials around the world began testing positive, including some Brazilian aides who dined and took pictures with Trump at his Mar-a-Lago Club in Florida.
The president and and vice president said they wouldn't be tested then because they weren't exhibiting symptoms.
Before his tone turned more serious regarding the virus, Trump downplayed it compared to the flu and said Democrats were trying to politicize it as a "hoax" to damage him politically.
In March, as the virus' reach in the U.S. and around the world became more clear, Trump also appeared hesitant to embrace the social distancing norms that have now become commonplace, such as not shaking hands.
Later, when the Centers for Disease Control and Prevention recommended people should be wearing cloth face masks in public, the president immediately said he wouldn't and has so far avoided doing so in public, in contrast to Pence.
Trump's daughter and senior adviser Ivanka Trump self-quarantined and worked from home for about a week in mid-March after she interacted with an Australian official at the White House who later tested positive for the virus.
The CDC recommends "wearing cloth face coverings in public settings where other social distancing measures are difficult to maintain."
CNN reports Thursday that the White House wasn't enforcing strict social distancing for its staff members and that few people, including the president's valets, wear masks while inside the building.
Trump told reporters earlier in the week before boarding Air Force One that he wasn't worried about being in close proximity with others on the plane.
"The test result comes back in five minutes and we have great testing, or they wouldn't be allowed to travel with me," Trump said. "It's not my choice. It's a very strong group of people that want to make sure they are tested, including Secret Service."
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