Japanese Prime Minister Shinzo Abe issued an emergency declaration this week to battle the virus, putting the country under restrictions after it seemed it had avoided the spread.
"I don't think anyone would be able to say if it is going to be possible to get it under control by next July or not," Tokyo organizing committee CEO Toshiro Muto said, speaking through an interpreter at a news conference conducted remotely. "We're certainly are not in a position to give you a clear answer."
The Olympics were postponed last month with a new opening set for July 23, 2021, followed by the Paralympics on Aug. 24.
Abe has been criticized for being slow to act against the coronavirus. Opposition political leaders have suggested he downplayed the severity of the virus and have said it may have been tied to wanting to hold the Olympics this year.
"We have made the decision to postpone the games by one year," Muto added. "So this means that all we can do is work hard to prepare for the games. We sincerely hope that come next year mankind will manage to overcome the coronavirus crisis."
Muto was asked if there are alternative plans to 2021.
"Rather than think about alternatives plans, we should put in all of our effort," he said. "Mankind should bring together all of its technology and wisdom to work hard so they can development treatments, medicines and vaccines."
Japan has reported about 5,000 cases and 100 deaths. The country has the world's oldest population, and COVID-19 can be especially serious for the elderly.
Muto was asked several times about the added costs of postponing, which has been estimated by Japanese media at between $2 billion-$6 billion. He said it was too soon to know the price tag and who would pay.
He also acknowledged that Tokyo Olympic organizers had taken out insurance.
"Tokyo 2020 has taken out several insurance policies," he said. "But whether the postponement of the games qualifies as an event that is covered is not clear yet."
He was also asked about the Olympic flame, which was taken off public display this week in Fukushima prefecture. Muto had an away-from-the-microphone talk with Tokyo spokesman Masa Takaya before talking about the flame.
"After the Olympic torch relay was canceled, the Olympic flame was put under the management of Tokyo 2020," Muto said. "Obviously in the future there is a possibility it might be put on display somewhere. However, for now it is under the management of Tokyo 2020 and I'm not going to make any further comment on the issue."
There are suggestions the International Olympic Committee is thinking of taking the flame on a world tour, hoping to use it as a symbol of the battle against the virus. However, any tour would be impossible until travel restrictions are lifted.
Taking the flame away from Japan could also upset the hosts.