"I played very well, I'm sorry for Richard, he is a good friend and a good person", Nadal said.
Fifth-seeded Argentine Juan Martin del Potro booked his place in the last 16 at Roland Garros for the first time in six years, with a straightforward 7-5 6-4 6-1 victory over Spain's Albert Ramos-Vinolas.
The Spaniard then recorded another convincing win in the second set, beating Gasquet 6-3, before ensuring he ran out a 3-0 victor thanks to a 6-2 win in the third set.
No. 3 Marin Cilic eliminated Steve Johnson of the U.S. 6-3 6-2 6-4.
"I'm disappointed to lose, you always want to do better, but I'm not frustrated", said the Frenchman.
It promises to be a hard-hitting match, with big serves and booming forehands, when Isner meets del Potro in the fourth round.
Halep performed remarkably in into the last-32 of the tournament after easing past America's Taylor Townsend in straight sets 6-3, 6-1.
Nadal was then untouchable on serve during the next two sets, with his serve never once in danger, while he broke his rival's serve two times in each set.
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He will next face 11th seed Diego Schwartzman after the diminutive Argentine underlined his clay court capability with a 7-5 6-3 6-3 victory against the unseeded Borna Coric.
Sixth seed Kevin Anderson is a potential quarter-final opponent for Nadal after beating Mischa Zverev 6-1 6-7 (3-7) 6-3 7-6 (7/4).
Should he and Fognini, who is also through to the round of 16 this year, both reach the quarterfinals, it will be the 2nd time in the Open Era that Italy has had multiple representatives in the quarterfinals of the men's singles at a Grand Slam. Will Halep make it third time lucky? He'll next face No. 11 seed Diego Schwartzman, a 7-5, 6-3, 6-3 victor against Borna Coric.
There was more French despair in the delayed match between Belgian eighth seed David Goffin and France's Gael Monfils, who squandered four match points before losing a closely-fought encounter. The big-serving Croat next faces No. 18 Fabio Fognini, who beat Kyle Edmund, 6-3, 4-6, 3-6, 6-4, 6-4.
The 27th seed insisted he doesn't respect Nadal too much on court, though, pointing out that he's not the first man to struggle against the 10-time French Open champion."It's not a question of respect".
Their third-round match at the French Open on Saturday followed a familiar pattern: Nadal subjected Gasquet to a 6-3, 6-2, 6-2 pummeling.