Two months before the Olympics are scheduled to begin in Paris, the global agency tasked with policing doping in sports is facing a growing crisis as it fends off allegations it helped cover up the positive tests of elite Chinese swimmers who went on to compete — and win medals — at the last Summer Games.

The allegations are particularly vexing for the World Anti-Doping Agency, which has long billed itself as the gold standard in the worldwide movement for clean sports, because they raise the specter that the agency — and by extension the entire system set up to try to keep the Olympics clean — cannot be trusted.

Athletes are openly questioning whether WADA can be relied upon to do its core job of ensuring there will be a level playing field in Paris, where some of the same Chinese swimmers are favorites to win more medals.

And in recent days, pressure on WADA has increased significantly, particularly from the United States, which is one of the agency’s chief funders, and as new questions have emerged about WADA’s appointment of an independent prosecutor to investigate the allegations, and whether WADA has provided an accurate account to the public about the appointment, according to interviews and documents reviewed by The New York Times.

On Wednesday, the Biden administration’s top drug official — who is also a member of WADA’s executive committee — sent a stinging letter to the antidoping agency laying out how it needs to appoint a truly independent commission to investigate how the positive tests were handled and demanding that its executive board hold an emergency meeting within the next 10 days.

“Let me underscore the extreme concern I have been hearing directly from American athletes and their representatives on this issue,” the official, Dr. Rahul Gupta, wrote in the letter, which was sent on Biden administration letterhead. “As I have shared with you, the athletes have expressed they are heading into the Olympic and Paralympic Games with serious concerns about whether the playing field is level and the competition fair.”