Tokyo 2020 President Yoshirō Mori claimed the Olympic and Paralympic Games would be "scrapped" if they could not be held next year.
Competition was postponed until 2021 last month due to the coronavirus pandemic, with the Olympics set to take place from July 23 to August 8 and the Paralympics scheduled for August 24 to September 5.
There are concerns that the pandemic may still be an issue next year, however.
In an interview with Japanese sports newspaper Nikkan Sports, Mori was asked whether Tokyo 2020 would be delayed again if it could not take place in 2021.
"No," he said.
"In that case, the Olympics will be scrapped.
"We have delayed the Olympics until next summer after we will have won the battle.
"The Olympics would be much more valuable than any Olympics in the past if we could go ahead with it after winning this battle.
"We have to believe this otherwise our hard work and efforts will not be rewarded."
Mori has already warned that the Games could not be rescheduled again, while International Olympic Committee member Richard Pound recently said he believed 2021 will be the only chance for Tokyo 2020 to take place.
Japan Medical Association President Yoshitake Yokokura has added fuel to the fire, claiming Tokyo 2020 could not be held next year if a vaccine against coronavirus has not been developed.
"My opinion is that it will be hard to host them unless an effective vaccine is developed," he said, as reported by Kyodo News.
"The global state of infections at that particular time will be a key issue.
"It will be difficult even if the situation in Japan has become better if infections continue to spread abroad."
The cost of the postponed Tokyo 2020 is also expected to be an issue.
Neither the IOC nor Tokyo 2020 have given any details regarding the cost of postponing the Games, although it has been reported it could be as high as $3 billion (£2.4 billion/€2.8 billion).
In his interview with Nikkan Sports, Mori suggested the Olympics and Paralympics may share Opening and Closing Ceremonies to save costs.
There are normally separate ceremonies for each event.
Tickets have already been sold for all four ceremonies, however, complicating Mori's idea.