Agassi, champion in 1994 and 1999 and seeded seventh, faces Croatian Ivo Karlovic, the world number 94.
Karlovic upset Lleyton Hewitt, the then defending champion, in the first round at Wimbledon in 2003 and recently reached the quarter-finals in Washington.
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Women's second seed Davenport, runner-up at the Australian Open and Wimbledon this year and winner at Flushing Meadows in 1998, continues her title bid against Pauline Parmentier of France.
Belgian seventh seed Justine Henin-Hardenne, the 2003 champion, plays Spaniard Maria Sanchez Lorenzo, while third seed Amelie Mauresmo of France takes on 16-year-old Sesil Karatantcheva of Bulgaria.