The standoff over free speech between the International Olympic Committee and U.S. Olympic officials continued on Tuesday, as the I.O.C. grappled with what to do if the Americans refused to penalize an athlete for violating rules limiting demonstrations on the medal podium.

On Sunday night, Raven Saunders, a U.S. shot putter, delivered the first political demonstration on the podium at the Tokyo Olympics when she raised her arms and crossed them in the shape of an X shortly after receiving her silver medal.

She made the gesture as the ceremony concluded, during a session for photographers after the medals were handed out and the Chinese national anthem had been played for the winner, Gong Lijiao.

As Saunders left, she told reporters that her act was “for oppressed people.”

Mark Adams, the chief spokesman for the I.O.C., said on Monday that leaders of the two organizations and World Athletics, track and field’s international governing body, were in talks.

“We want to fully understand what is going on with the matter and take it from there,” Adams said.

Kate Hartman, the chief spokeswoman for the United States Olympic and Paralympic Committee, said the organization’s leaders had pointed out to I.O.C. officials that Saunders did not perform her demonstration during the awarding of the medals or the playing of the Chinese anthem.

“That is important to us,” Hartman said.

The I.O.C. and the U.S. Olympic Committee have conflicting rules and views regarding the exercise of free speech during the Games, and even how penalties should be meted out.

The I.O.C., which prohibits demonstrations on the podium or during competition, said on Sunday night that an athlete’s national Olympic committee is required to issue any required punishment. U.S. officials have said they will not punish any athlete for exercising the right to free speech that does not express hatred.

Sarah Hirshland, the chief executive of the U.S. Olympic Committee, said last week that international Olympic leaders “have the authority and the jurisdiction and a unique set of sanctions. We sit in a different seat.”

If the I.O.C. orders the Americans to punish an athlete and they refuse to do so, they would be in violation of the Olympic charter.

Also on Sunday, Race Imboden, an American fencer, went to the podium at a different venue after the United States took the bronze medal in foil with a circled X written on his hand. But Hartman said no one had complained about the episode.

Asked what would happen next, Hartman said, “Now we wait.”

By waiting, though, the U.S. Olympic Committee is behaving far differently that American Olympic leaders did in 1968 and 1972, when they moved quickly to punish Black athletes who demonstrated on the podium or did not behave according to the I.O.C.’s standards, forcing them to leave the Games.

World Athletics is also highly unlikely to discipline athletes because the federation does not have any rules against demonstrations on its books. Sebastian Coe, the federation’s president, said this year that he was “reluctant to discourage athletes from expressing their views, and I sense that the current generation is more willing to speak out than some previous generations were.”

U.S. officials are trying to eliminate the free speech issue before the Summer Games come to Los Angeles in 2028.