Faced with growing frustration from athletes and some national committees, the International Olympic Committee said it would decide within four weeks on the Tokyo Games.

The International Olympic Committee, faced with mounting pressure to postpone the Summer Olympics in Tokyo, said on Sunday that it would decide within four weeks whether to delay or scale down the Games.

Yet not long after it announced its timeline, support for having the Games this summer continued to crumble as Canada said it would not send its athletes, Australia told its athletes to prepare for a rescheduling of the event to 2021 and Prime Minister Shinzo Abe of Japan acknowledged the Olympics might not go on as planned.

“I couldn’t think of cancellation,” Abe told members of Parliament. But, he added, if it were not possible to hold the Games as scheduled, “I think we may not have a choice but to make a decision to postpone, putting a priority on athletes.”

The I.O.C. statement on Sunday reiterated the position of Thomas Bach, president of the organization, that canceling the Games altogether was not an option and sought to address complaints that the committee had not been transparent in how or when a decision would be made.