Only 20 minutes of the day session at the U.S. Open were played because of a second day of rain. (Mel Evans/AP)

The rain that has drenched the northeast the past two days escalated from mild inconvenience to major disruption Wednesday at the U.S. Open, imperiling an orderly conclusion to the tournament and creating a glaring competitive disadvantage in the men’s field.

On the heels of Tuesday’s total washout, only 20 minutes of tennis were contested Wednesday. And more rain is forecast Thursday.

It was a controversial 20 minutes of play at that, with three of the sport’s biggest names — Rafael Nadal, the tournament’s defending champion; 2003 champion Andy Roddick; and 2008 runner-up Andy Murray — sent out to play their fourth-round matches under a heavy mist, with the courts still damp.

Nadal’s unease was evident as he stepped onto Arthur Ashe Stadium at 12:20 p.m.

After roughly 20 minutes, both Nadal and Roddick raised concerns about the slick conditions to the chair umpire on their respective courts. Nadal trailed Gilles Muller 0-3 at that point, having been broken at love in his opening service game. Roddick, playing David Ferrer on Louis Armstrong Stadium, led 3-1. Murray’s match against American wild-card Donald Young was on serve, with Young leading 2-1.

When tournament referee Brian Earley stepped out to examine the court on Ashe, the normally well-mannered Nadal, according to ESPN’s Pam Shriver, reporting courtside and within earshot, said: “It’s the same old thing. All you think about is money.”

After Earley suspended play on all courts, Nadal, Murray and Roddick requested a closed-door meeting to express their frustration over being asked to play on slippery courts that risk serious ankle and knee injuries.

Roddick later told Shriver that players made clear it would be “uncomfortable” if they were asked to play in comparable conditions in the future.

“He listened to what we had to say,” Roddick told ESPN. “How far that went, I don’t know.”

Other accounts of the meeting indicated that the players flatly said they wouldn’t play on damp courts.

Former touring pro Justin Gimelstob, the players’ representative on the ATP Board of Directors, explained the concern.

“You either feel safe on court or you don’t,” Gimelstob said in an interview. “The way these big, strong athletes move and stop and start — and the energy and explosiveness involved — there is no 99 percent safe. They’re 100 percent safe or not at all.”

Asked how much voice players have in such scheduling decisions, Hall of Famer Mats Wilander, the 1988 U.S. Open champion, said: “I think [the tournament is] taking into consideration the player who decides not to play. But that is a big step to make for a player. But in today’s world, I think the players would not be afraid to say, ‘I’m not doing it. I’m just not playing.’ I don’t think the U.S. Open can afford to have players go out and say that about their tournament. Nadal, Murray — they are too big names to come into conflict.”

Gimelstob, also a Tennis Channel analyst, said he was particularly concerned about the competitive imbalance caused by the out-of-sync schedule on the men’s side, with half the field facing the prospect of playing four matches in four days.

“It’s a very physical tournament because it’s hot, humid and hard-court tennis is inherently physical,” Gimelstob said. “Then, under a normal schedule, you throw in Saturday-Sunday back-to-back men’s semifinals and finals, which no other tournament does. When you throw rain on top of that, it’s an absolute recipe for disaster. And that’s what we have now.”

The scheduling woes may well be compounded in the coming days, with rain forecast for Thursday and Friday, as well.

Tournament director Jim Curley said officials would do everything possible to complete the tournament on time. Curley said absolutely no consideration would be given to paring men’s matches from best-of-five sets to best-of-three sets, but he didn’t rule out the possibility of asking men or women to play two matches in one day.

After attempting to stage the women’s quarterfinals during a brief dry spell that was forecast Wednesday night, tournament officials canceled the evening session at 8:16 p.m. when rain returned as Serena Williams and Anastasia Pavlyuchenkova were warming up.

The scheduling upheaval has rekindled criticism of the U.S. Tennis Association for failing to anticipate the need for a retractable roof when 23,500-seat Arthur Ashe Stadium was constructed in 1997 and for its lack of a viable plan for constructing a new venue with a roof.

In 2009, Wimbledon unveiled its Centre Court roof. The Australian Open has a venue with a roof that can be deployed to shield players from heat or rain. The French Open is planning to construct a roof.

According to Curley, adding a roof to Ashe, the most cavernous venue in tennis, is cost-prohibitive and technically challenging, if not impossible.

“Going back in time, do I wish there was a roof over Ashe? Absolutely!” Curley said. “I wish I had four of them. But we don’t. We play the cards that we have.”