The admission was based on audio recordings released Wednesday from interviews with senior US journalist Bob Woodward.
"I wanted to always play it down," Trump said in an interview with Woodward on March 19, according to a CNN preview of the book "Rage", due to be published September 15.
"I still like playing it down because I don't want to create a panic," he said in the conversation with Woodward, which was recorded.
In another recorded interview, on February 7, he told Woodward the virus "goes through the air" — despite repeatedly mocking people who wear masks in the weeks and months after. It took until July before he was seen publicly wearing a mask.
Coming eight weeks before the November 3 presidential election, the revelations add new pressure on Trump.
Opinion polls show around two-thirds of Americans disapprove of his handling of the virus and he has often been accused of minimizing the crisis in order to try and boost his reelection chances.
Speaking to reporters at the White House, Trump denounced the book as "another political hit job" and said if he'd downplayed Covid-19 it was to prevent a "frenzy".
"I don't want people to be frightened," he said.