While the tournament continues, WTA chief Larry Scott said the lucrative event risks being taken off the schedule for violating the principle that sports and politics should not mix.
Peer was scheduled to play Anna Chakvetadze of Russia on Monday, but was back in Israel and issued a statement that expressed her disappointment in being prevented from competing.
"I think a red line has been crossed here that could harm the purity of the sport and other sports,'' Peer said.
Vesnina defeated Kuznetsova 6-4, 3-6, 6-0 in 1 hour 41 minutes in the second-round match. Ayumi Morita of Japan, who replaced Peer in the draw, defeated the 15th-seeded Chakvetadze 7-5, 6-2 and ninth-seeded Agnieszka Radwanska of Poland lost to her younger sister, Urszula, 6-4, 6-3 in first-round matches.
Also, French Open champion and eighth-seeded Ana Ivanovic of Serbia moved into the third round with a 7-5, 6-4 win over Alisa Kleybanova of Russia.
Amelie Mauresmo, winner of last week's Paris Open, withdrew at the last minute and was fined $7,500 by the WTA.
Vesnina, ranked 75th in the world and a qualifier here, was thrilled with her victory.
"She's obviously a top 10 player, so it's even more special,'' the 22-year-old Russian said. "I think I really troubled her today. She wasn't comfortable at all and I feel she was totally lost in the third set. She kept looking at her coach.''
Kuznetsova said the fast court was a problem.
"The court was fast, and I just could not get the feel of the ball throughout the match,'' Kuznetsova said. "I am now off to Moscow, and I really need to work hard on my game.''
The event has attracted a quality field this year with most of the top 10 competing. Australian Open winner Serena Williams is the top seed.
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