Mr. Trump received a positive result on Thursday evening before making an appearance on Fox News in which he didn’t reveal those results. Instead, he confirmed earlier reports that one of his top aides had tested positive for coronavirus and mentioned the second test he had taken that night for which he was awaiting results…

Under White House protocols, the more reliable test that screens a specimen from deeper in the nasal passage is administered only after a rapid test shows a positive reading. Based on people familiar with the matter, the president’s tests followed that protocol.

As the virus spread among the people closest to him, Mr. Trump also asked one adviser not to disclose results of their own positive test. “Don’t tell anyone,” Mr. Trump said, according to a person familiar with the conversation.

Mr. Trump and his top advisers also aimed to keep such a close hold on the early positive results that his campaign manager, Bill Stepien, didn’t know that Hope Hicks, one of the president’s closest White House aides, had tested positive on Thursday morning until news reports later that evening, according to a person familiar with the matter. The Trump campaign said Friday evening that Mr. Stepien had tested positive.