NEW YORK — Caroline Wozniacki of Denmark was seeded No. 1 at a Grand Slam tournament for the first time Tuesday, getting the top spot at the U.S. Open because Serena Williams pulled out with a foot injury.

Wozniacki, ranked No. 2 behind Williams by the WTA, was the runner-up at Flushing Meadows last year and is the first woman since 2003 to be seeded No. 1 at the U.S. Open without already having won a major championship.

Defending champion Kim Clijsters was seeded No. 2 by the U.S. Tennis Association, which stuck strictly to the rankings in determining the seedings. Venus Williams, the 2000-01 U.S. Open champion, is No. 3, followed by 2008 runner-up Jelena Jankovic and French Open runner-up Sam Stosur.

Two other past U.S. Open champions who were seeded are No. 11 Svetlana Kuznetsova and No. 14 Maria Sharapova.

Serena Williams, Venus’ younger sister, withdrew last week, saying she still is recovering from surgery to repair cuts on her right foot.

The men’s seedings were announced Monday, with Rafael Nadal at No. 1, and Roger Federer at No. 2. The 2009 men’s champion, Juan Martin del Potro, withdrew Saturday because he isn’t ready to compete after undergoing an operation on his right wrist in May.

The announcement of the women’s seedings was delayed a day because Sunday’s final at the Rogers Cup in Montreal was rained out. Wozniacki wound up winning Monday’s final for her third title of 2010.

The draw for the U.S. Open is Thursday. Play begins Monday.