The White House personnel office has said that staff must cover their faces at all times except when seated at their desks, socially distant from colleagues.
The directive comes after an aide for Vice-President Mike Pence and a valet for President Trump fell ill.
Mr Trump said he required the policy.
Appearing without a mask in the Rose Garden for a press briefing on Monday, however, the president claimed he did not need to follow the directive because he kept "far away from everyone", and played down the White House infections.
"We have hundreds of people a day pouring into the White House" each day, he said. "I think we're doing a good job containing it."
Three members of the White House coronavirus task force went into self-isolation for two weeks after possible exposure to the illness.
They include Dr Anthony Fauci, who has become the public face of the fight against the virus in the US.
Mr Trump shrugged of the White House spread, saying it was "basically one person" who had contracted the virus and that people who were in contact had since tested negative.
Mr Trump said more funds would be made available to increase testing in states.
The government is to provide $11bn (£8.9bn) to states to meet testing goals this month. States were asked how many tests they hope to conduct in May, and will be given supplies to match the targets.
Pressed by journalists on when all Americans could expect to have access to testing, Mr Trump said: "If someone wants to be tested right now they will be able to be tested". The claim is heavily disputed.
"We have a lot of people coming in and out," he said. "We are running a country."