Novak Djokovic defeated Ernests Gulbis 5-7, 7-6 (9/7), 6-1 but Rafael Nadal failed to go past high-flying Kei Nishikori.
Roger Federer defeated wild card Peter Polansky 6-2, 6-0. Stanislas Wawrinka, Ernests Gulbis and Richard Gasquet also advanced.
He is making his 13th appearance at the pre-Wimbledon warm-up and took the title for the first time in 2012, beating Roger Federer in the final.
Murray's admission chimes with an accusation from Latvia's Ernests Gulbis that the big four of men's tennis -- Murray, Novak Djokovic, Roger Federer and Rafael Nadal -- are "boring".
A former top 10 player, Monfils missed the French Open last year because of a right knee injury. His best showing at Roland Garros was a semifinal finish in 2008.
He will next face compatriot David Ferrer, who advanced in a walkover against Philipp Kohlschreiber, who was suffering from vertigo.
Gulbis, who was 21 in the world two years ago, jumped ahead 4-1 in the tie-breaker before each man won two points on his own serve and Roger-Vasselin went wide with a backhand to drop the set.
Michael Llodra was slapped with a $2,500 fine for using a racial slur during his opening-round match against Ernests Gulbis at the ATP Tour's Indian Wells tournament, officials said on Sunday.
Latvia's Ernests Gulbis earned the second ATP title of his career Sunday, rallying to upset top-seeded American Mardy Fish 5-7, 6-4, 6-4 to win the $619,500 Los Angeles hardcourt crown.
James Blake rallied to win a second-set tiebreaker and overcame a 1-hour, 18-minute rain delay on Monday night for a 5-7, 7-6 (5), 6-2 victory over Ernests Gulbis of Latvia in the first round of the Atlanta Tennis Championships.
Two-time major winner Novak Djokovic finished off his demolition of Ernests Gulbis in Indian Wells with back-to-back aces to reach the fourth round on Tuesday.