It said Trump and Vice President Mike Pence have since tested negative for the virus and "remain in good health".
The White House was moving to shore up its protection protocols to protect the nation's political leaders.
"I've had very little contact, personal contact, with this gentleman", said Trump at the Oval Office.
Why it matters: Trump noted that the administration may seek to "add or subtract people.as appropriate" - adding to concerns that the White House could oust medical officials as it seeks to reframe the pandemic as an economic crisis.
"It's possible there will be some because you won't be locked into an apartment or a house or whatever it is", Trump said, before criticizing "out of whack" models.
Trump had said on Tuesday he planned to replace the task force with "something in a different form".
Trump has praised governors of states that have started to loosen restrictions on social distancing and business activity, even though he has admitted that people will suffer as a result. "Yeah it's a little bit odd, but it's one of those things", he said.
Elon Musk Reveals How to Pronounce Baby X Æ A-12′s Name
You really just have to say each letter and number individually, like reading a damn license plate. "So its just X, the letter X, then the Æ is pronounced "ash".
Public health experts warn of a new surge in cases if reopenings occur without vastly expanded diagnostic screening and a system to trace who has been in contact with newly infected patients so that they are also isolated and tested.
White House staff working in the West Wing have not been wearing masks around the president or each other.
"But they do the tests and it just shows you that the fallacy - it is what I have been saying - testing is not a ideal art".
The White House began instituting safety protocols almost two months ago, including frequent temperature checks.
Mr Trump has now been tested at least twice for coronavirus and both times tested negative.