The fate of the 2020 Games, scheduled to open in Tokyo on July 24, has been thrown into doubt by the outbreak of the virus, now dubbed a pandemic.
But organisers, Japanese government officials and the International Olympic Committee have insisted preparation for the Games is on track, with no expectations of a postponement or cancellation.
"There is no change in the government policy in that we closely cooperate with the IOC, the organising committee, and the Tokyo metropolitan government to steadily prepare for holding the Games as scheduled," government spokesman Yoshihide Suga told reporters.
He said Prime Minister Shinzo Abe and Trump had held a phone call to discuss the outbreak as well as the Olympics.
"In the telephone talks with President Trump, the prime minister mentioned our efforts toward holding the Games, and the president said he highly values Japan's efforts on transparency," Suga said.
He did not say whether Trump had repeated his suggestion, made a day earlier, that the Games might need to be delayed.
"I would say maybe they postpone it for a year," Trump told reporters in the Oval Office on Thursday.
"You know, I like that better than I like having empty stadiums all over the place. I think if you cancel it, make it a year later, that's a better alternative than doing it with no crowd," he said.
The suggestion was roundly dismissed by Japan's Olympic minister Seiko Hashimoto.
"I'm aware of President Trump's remarks but neither the IOC nor the organising committee is thinking about delaying or cancelling the Games at all," she said at a regular briefing Friday.
Asked about the possibility of scaling back the number of spectators, Hashimoto said: "We are not thinking about that at all."
Suga also said the government "doesn't envisage" either a Games without spectators or the prospect of athletes withdrawing from the event.
IOC chief Thomas Bach told German television ARD on Thursday that the body would follow recommendations by the World Health Organization, but for now continues to work for a "successful" Games.
He acknowledged however that cancellations of Olympic qualifiers are starting to pose "serious problems".