Williams's was bidding for a record-equalling 24th Grand Slam singles in Paris but the 10th seed was knocked out 6-2 7-5 by fellow American Kenin.
It was the 23-time Grand Slam title winner's earliest exit at a Slam in nearly five years and she was eager to be away from the tournament site as quickly as possible.
Williams had fourth-ranked men's player Dominic Thiem booted from the main interview room before he was finished his post-match press conference because she didn't want to wait for him to finish, according to Ben Rothenberg of The New York Times.
Only four of the women's top 10 seeds are left in the tournament among them are three-time victor Serena Williams and defending champion Simona Halep.
Williams couldn't control her shots, compiling 34 unforced errors, twice as many as Kenin's 17.
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Secretary of State Mike Pompeo by phone and said face-to-face talks between the two would take place on Wednesday in Washington. He nevertheless noted that Mexico reserved the right to seek worldwide legal arbitration to resolve the dispute.
One key statistic: Osaka compiled seven break points in the first set but failed to convert a single one.
"Honestly, if Serena didn't lose this one she would probably lose next round, or when the top players would have been the other side of the court".
"She played really well", Williams said.
Sofia Kenin's 6-2, 7-5 win over Williams and Katerina Siniakova's 6-4, 6-2 victory over Osaka underscored the wide-open nature of women's tennis.
Siniakova took control in the second set, converting the first of two break points to go 3-2 up.
She had won her past 16 matches at majors, allowing her to lift the trophies at the U.S. Open last September and Australian Open in January. "I was very solid", said Monfils.
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"At this time it is believed that only one shooter, and they have been taken into custody". This is a breaking news report - we will have additional details as they become available.
But Osaka said Saturday that she felt exhausted and was dealing with a headache.
Despite being seeded top for the first time at a Slam, Osaka never looked convincing in Paris.
"I don't know exactly what happened".
That pattern continued here and she could not find a way back against the world No 42, who prevailed 6-4 6-2. So I think it will be enough time. "So everything definitely feels a little bit harder than normal, but at the same time, I know that it's going to get better".
Gael Monfils defeated Antoine Hoang in straight sets, 6-3 6-2 6-3, to reach the French Open fourth round and book a clash against the defending finalist Dominic Thiem.
Williams, meanwhile, opened slowly in Paris and had to scramble from a set down to win her first match against Vitalia Diatchenko, then dispatched Japanese qualifier Kurumi Nara in more routine fashion - although nothing is coming particularly easy for her this season.
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