Ivanovic, who was the top-ranked player for 12 weeks in 2008, has dropped to No. 8 in the world ranking but believed she had chances to repeat her feat at Roland Garros last year.
"I did it in the past so I believe I have time to do it again. I love playing here on these courts on the clay. I just have to keep my head down and work tough through the matches," she said.
"There are so many players who want to achieve the same thing, but I believe I have quality and I
have to go with this confidence for each match."
The 25th-seeded Li Na of China became the first player to reach the second round after a 6-4, 6-2
quick win over Poland's Marta Domachowska.
The 27-year-old, who missed the Australian Open and withdrew from this week's Strasbourg because of injury, needed just 72 minutes to make the second round where she will face Switzerland's Timea Bacsinszky.
Five Russians moved into the next round including Nadia Petrova, who cruised through to a possible second round clash against compatriot Maria Sharapova.
The 11th seed beat Lauren Embree 6-1, 6-2. She clearly dominated the game as she hit 27 winners to her opponent's three.
Petrova was joined by fellow Russians 17-year-old Anastasia Pavlyuchenkova, the 27th seed, and 18-year-old qualifier Vitalia Diatchenko.
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