The statement said the Osaka segment would be conducted in the park "for all torchbearers who wish to run there." It also said "no spectators" would be admitted either day.
The ordeal of keeping the relay on track reminds of the giant problems that are likely when the Olympics and Paralympics take place with a total of 15,400 athletes from more than 200 countries entering Japan. They will be joined by tens of thousands of other officials, judges, media and broadcasters.
Fans from abroad are banned, and it is not yet clear how many local fans will be able to attend Olympic events. Tokyo organizing committee president Seiko Hashimoto promised a decision this month on venue capacity, but hinted last week that the announcement could be delayed.
Ticket sales were to account for $800 million in revenue for the organizers, a large chunk but small compared to the official bill for the Olympics of $15.4 billion, most of which falls on Japanese taxpayers.
Osaka prefecture Governor Hirofumi Yoshimura asked people on Wednesday not to make unnecessary trips in the area.
"Medical systems (in Osaka) are on the verge of collapse," Yoshimura said at a news conference, attributing the rapid spike in infections to new variants of the virus. "Obviously it spreads more rapidly and it is more contagious."
About 70% of hospital beds available in Osaka have already been occupied, officials said.
Osaka reported 719 new cases Tuesday and more than 800 were expected Wednesday, both exceeding totals for Tokyo. But there are also fears the spike will be seen soon in Tokyo.
The vaccine rollout is extremely slow in Japan with very few people expected to be vaccinated when the Olympics begin. Japan has attributed about 9,300 deaths to COVID-19, which is good by world standards but poor by the standards in most Asian countries.