The unannounced doping tests were organised during the training camp in Saint-Cyprien for French athletes, the International Judo Federation said in a statement on Tuesday.
The controller was surprised to also meet foreign athletes who had been training with the French and decided to test them by asking for their judo results in order to test the world's best athletes, the IJF said.
"Coaches from several countries were surprised by the procedures of this control and asked for advice from the IJF anti-doping specialist," the federation said.
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"She cautiously expressed that in view of the reported facts, they had no obligation to do the test in those conditions."
Amid doubts over the testing, some athletes underwent tests while others, like Kelmendi and Martyna Trajdos of Germany, did not.
When informed about the case, IJF President Marius Vizer decided to test those who did not submit to the testing the following week, and the results were negative, the IJF said.
The Guardian newspaper on Monday quoted Agron Kuka, head of the Kosovo Judo Federation, as saying that Kelmendi had refused the drug test but that she was clean.
"The team was in the training camp in France and some person came and asked to do the doping control.
"But the person involved, she didn't have any authorisation from WADA or anyone. And that's the end of the story."
The IJF confirmed to Reuters that Kelmendi had taken several drug tests this year, including in Rio on Sunday, the day she became the first athlete from Kosovo to win an Olympic medal.
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