TOKYO — A week ago, Prime Minister Shinzo Abe of Japan and Thomas Bach, president of the International Olympic Committee, were promoting the Summer Olympics in Tokyo as the balm the world needed to show victory over the coronavirus pandemic.

On Tuesday, the virus won out.

Bach and Abe bowed to a groundswell of resistance — from athletes, from sports federations, from national Olympic committees, from health experts — and formally postponed the Games, which had been scheduled to begin in late July, until 2021.

The decision brought both a sense of relief and impending chaos to international sports.

Abe broke the news after a phone call with Bach, when complaints that the I.O.C. was not moving quickly enough to adjust to the coronavirus pandemic became too loud to ignore.