More bad weather at the US Open is likely to push back the men's final to Monday.
Rain has forced many delays
Tournament organisers issued the warning after observing Thursday's forecast for more rain in the New York area.
Three days of showers at Flushing Meadows have already led to the postponement of four women's and three men's quarter-final matches.
And Wednesday's delays appear to have ended hopes of completing the year's final Grand Slam on time.
Only 15 minutes of action - between top seed Kim Clijsters and Amelie Mauresmo - was possible in the early session.
Seven hours later, American Andy Roddick wrapped up a 6-3 6-4 7-6 victory over Belgium's Xavier Malisse though they had to leave the court for an hour as the rain returned.
The decision to abandon the day session on the tenth day of action means Ai Sugiyama's fourth-round match against Francesca Schiavone will be carried over to a fourth day, as will seventh seed Anastasia Myskina's match with Mary Pierce.
"We are doing our best to finish the tournament on time, but the challenge has got all the more challenging," said USTA president Arlen Kantarian.
"We are determined to make the best of a very difficult situation."
Clijsters, who seized a 3-0 lead over fifth seed Mauresmo, expects to finish her quarter-final on Thursday.
And Lindsay Davenport and Paola Suarez hope to advance beyond the warm-up stage of their delayed match
"It is a little taste of Wimbledon-like weather," said Pierce.
"With Wimbledon it's not as bad because if you stay in
the village you can stay in your place, hang out. Sometimes it's crazy with a lot of girls waiting around here."
In the men's draw, Paradorn Srichaphan's match against Australia's Lleyton Hewitt, Guillermo Coria encounter with Jonas Bjorkman and Juan Carlos Ferrero's game against Todd Martin are scheduled for Thursday.