Three of the four outstanding last-16 games - including the clash between Andy Murray and Donald Young - did get under way but only around 15 minutes of play were possible before rain, which had delayed the start by 90 minutes, returned to Flushing Meadows.
Just after 5.30pm local time (2230 BST), organisers admitted defeat and cancelled the four matches which will now be rescheduled for Thursday.
The men's quarter-finals slated for Wednesday had earlier been pulled from the schedule.
A tournament statement read: "Unfortunately, due to the lingering rain, the day session has been cancelled."
Earlier the opening three games of Murray-Young had gone with serve, the American being 2-1 up when the rain came.
Defending champion Rafael Nadal struggled in the damp conditions and was 3-0 down to Gilles Muller, while Andy Roddick was 3-1 up on David Ferrer.
The inability to get those matches finished leaves Murray, Nadal et al facing the prospect of playing four matches in four days unless the final - currently scheduled for Sunday - is put back.
Even that may prove fanciful with more bad weather forecast for New York in the coming days.
Murray urged organisers to push the tournament into a third week.
Speaking before a final decision about cancelling Wednesday's play had been made, Murray told Sky Sports: "If we don't (finish today), I think they should move it to Monday.
"With each minute that passes its more of a disadvantage for us, potentially having to play four matches in four days.
"I don't remember the last time that would have happened in a slam and it's an incredibly difficult thing to do. We want to get out there, there's talk of maybe moving the final to Monday, which would help a little bit.''
Meanwhile, after returning to the locker room, both Murray and Nadal accused organisers of compromising their safety.
Nadal, Murray and Roddick all went to see tournament referee Brian Earley to complain about the situation.
Defending champion Nadal told ESPN: "They called us on court to start the match and the rain hadn't even stopped.
"I understand the fans want to see tennis but the health of the players is the most important and we do not feel protected. We want to feel good when we are playing a tournament and we cannot accept these things.
"We have to fight to change things, to have enough power that we don't have to go on court when it's raining. If I have to go on court, I'll go on court, but I don't think it's fair."
Murray aded: "When we went out on court it was still wet, and the balls too. It doesn't make sense to get out there for seven or eight minutes and I don't think that will happen again.
"I knew that Rafa was going to see (Earley). I said I would go in and mention it as well, then Andy (Roddick) came.
The United States Tennis Association, however, issued a statement defending the decision to send the players out.
"All parties, including the players and tournament, want to get the US Open back on schedule," read the statement.
"As of 12 noon today, the best information available to us indicated the chance of a two-hour window without rain. Unfortunately, not all light rain and mist shows up on radar.
"We have experienced referees, and they decide if courts are fit for play. Conditions may be not ideal, but still can be safe.
"However, if a player or players feel that conditions are unsafe, we listen to them, as we have always done, and the referee uses that information as part of his/her assessment on whether to continue or halt play."