Dr. Rodchenkov said that for at least 15 Russian athletes who won medals at Sochi, both the A and B samples were substituted before they were tested. None of the bottles’ caps — which are branded with unique seven-digit codes — showed any signs of having been opened.

Each night at Sochi, Dr. Rodchenkov said, sealed bottles were passed through a hole in the wall of the storage closet that served as his shadow laboratory. The bottles were handed to a man who he believed worked for the Russian intelligence service, the F.S.B. Within two hours, he said, those same bottles were returned to him, their caps unlocked.

“Magicians were on duty,” Dr. Rodchenkov said, suspecting that F.S.B. officers had studied the toothed metal rings that lock the bottle when the cap is twisted shut. According to him, they collected hundreds of them leading up to the Olympics.

Dr. Catlin theorized that heat had been applied to remove the bottles’ caps.

He said he had expressed some concern about the bottles years ago, asking if they could be outfitted with internal thermometers, to show if the sample had been frozen or heated. “But that’s just a wild guess,” he said.

After his account was published, Dr. Rodchenkov sent a letter to the World Anti-Doping Agency and the I.O.C., calling on them to examine the B samples of Russian athletes from the 2014 Sochi Games, whom he offered to help identify. Bryan Fogel, an American filmmaker who helped Dr. Rodchenkov flee to Los Angeles, where he now lives, also signed the letter.

While those samples would not contain traces of steroids, Dr. Rodchenkov told The Times, they would bear evidence of tampering. He said there would be scratch marks around the necks of the bottles, where the metal rings are.

He also said that common table salt could be found in some of the samples. When he replaced tainted urine with clean urine, he added salt or water to the new urine to match the chemical specifications of the original sample.