In other potential quarterfinal pairings, fourth seed Tim Henman of Great Britain would face fifth seed Juan Carlos Ferrero of Spain and Spanish third seed Carlos Moya would meet seventh-seeded German Rainer Schuettler.
Two-time winner Pete Sampras and Spain's Juan Carlos Ferrero have both asked for wild cards.
Federer made a slow start but recovered to get the better of Spain's Juan Carlos Ferrero 6-3 6-4.
But 2003 champion Juan Carlos Ferrero was forced to retire from his first-round match due to a leg injury.
Nicknamed the Mosquito, Juan Carlos Ferrero is a clay-court master who has firmly established himself at the top of the game.
Nadal will now face compatriot and ninth seed Juan Carlos Ferrero, who saw off fifth seed Jo-Wilfried Tsonga 6-1 3-6 7-5.
Earlier, champions Spain had secured a 2-0 lead over Israel thanks to convincing singles wins by Juan Carlos Ferrero and David Ferrer.
And he made 78 unforced errors as he slipped to defeat against Juan Carlos Ferrero in the semi-finals of the French Open.
Although still only 21, Federer is firmly established in the top 10 alongside other youngsters Lleyton Hewitt, Marat Safin and Juan Carlos Ferrero.
Within a few minutes, though, he was trailing Juan Carlos Ferrero a former No. 1 by a break of serve and missing many a forehand.
The 21-year-old will leapfrog Juan Carlos Ferrero when the rankings come out on Monday, and will also overtake the Spaniard in the Champions Race.
Former world number one Juan Carlos Ferrero of Spain made an early exit from the competition, beaten 4-6 6-2 6-4 by German Mischa Zverev .
And Andy Roddick took less than an hour to dispatch Juan Carlos Ferrero 6-2 6-4, serving 18 aces and conceding just 11 points on serve.
In the last four Federer will face sixth seed Andy Roddick , who beat Karol Kucera, conqueror of second seed Juan Carlos Ferrero, 7-6 6-3.
Gonzalez beat Juan Carlos Ferrero of Spain 6-2 6-1, Moya defeated Germany's Denis Gremelmayr 6-1 6-4 and 13th-seeded Berdych downed Russian Mikhail Youzhny 7-6 (3) 6-4.
The 2009 U.S. Open champion, from Argentina, will now face Croatian Marin Cilic after the No. 21 seed defeated Juan Carlos Ferrero of Spain 7-6 6-2 6-3.
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Federer is now in fifth place in the Champions Race standings, just 10 points behind Spain's Juan Carlos Ferrero who is already out of the Paris tournament.
Nadal heads to Italy on Monday for the Rome Masters, the location of his last defeat on clay when he lost to compatriot Juan Carlos Ferrero last year.
He will next play unseeded Spanish claycourt specialist Juan Carlos Ferrero, who ousted Chilean 10th seed Fernando Gonzalez 4-6 7-5 6-4 4-6 6-4 in an epic clash.
Fellow American James Blake beat Peter Polansky of Canada 6-7 (1-7) 6-3 6-2 6-4, while Spain's 22nd seed Juan Carlos Ferrero defeated Ricardo Mello of Brazil 6-1 6-4 6-4.
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Roddick, who will replace Juan Carlos Ferrero as world number one when the rankings are released on Monday, admitted he had not played well enough against an inspired opponent.
Thirteenth seed Radek Stepanek beat former world number one Juan Carlos Ferrero 6-3 6-0 in the first round on Monday, while 16th seed David Ferrer beat Richard Gasquet 6-4 6-3.
But Nalbandian demonstrated a baseline game with the kind of power off both sides that very few can match, and a forehand that bears comparison with that of Juan Carlos Ferrero.
Fourth seed Rafael Nadal beat fellow Spaniard and 15th seed David Ferrer 7-6 (7-5) 6-4 and will next face eighth seed Jo-Wilfried Tsonga, who trounced Juan Carlos Ferrero of Spain 6-2 6-2.
Hewitt joined another former world No. 1 in progressing as Juan Carlos Ferrero upset seventh-seeded Spanish Davis Cup teammate Tommy Robredo 6-3 6-2 to set up a clash with German 10th seed Tommy Haas.
The first came against Cedric Pioline in front of a hostile crowd in France, while the second installment saw him beat Juan Carlos Ferrero of Spain in front of a partisan crowd in his home town of Melbourne.
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Meanwhile, Nadal, bidding for an astonishing sixth successive victory in the principality, was made to work harder to defeat fellow-Spaniard Juan Carlos Ferrero 6-4 6-2 in a match that was held up for 30 minutes because of rain and high winds.
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