Nadal, Andy Roddick and Andy Murray all complained about the wet and dangerous court conditions and said they should not have started their matches Wednesday.
Fourth-round men's matches barely lasted 15 minutes before rain chased the players off the courts.
At the time of stoppage, Nadal was trailing unseeded Gilles Muller 0-3 after 16 minutes of tennis. Roddick, seeded 21st, was ahead of fifth-seed David Ferrer 3-1 and fourth-seed Murray was leading against wild card entry Donald Young 2-1.
The United States Tennis Association (USTA) officials wanted to carry on with the schedule of matches but the top players told them that they would only play when the courts were completely safe.
"We have to fight to change that, to have enough power to say we don't want go on court when it is raining," Nadal told ESPN.
"I am sorry for the fans, but the health of the players is important."
In the afternoon, USTA announced the cancellation of men's matches and later, the night session with a card of four women’s semi-final matches was also called off.
The first quarterfinal between three-time champion Serena Williams and 17th-seed Russian Anastasia Pavlyuchenkova could not get off as rain stopped them while they were warming up.
All the matches scheduled for Tuesday had also been cancelled.
For the delays, the tournament is now in danger of having a Monday finish for the fourth straight year.
The weather forecast for Thursday and Friday also suggests heavy doses of rain.
