Oliver Stone's film about the events of 11 September took $4.4m (£2.3m) on its opening day in North America, according to early studio estimates.
Oliver Stone directed the film, which was mostly shot in Los Angeles
Paramount Pictures said it was hopeful World Trade Center would beat expectations for its first weekend.
If the pace continued, it could go on to generate $20m (£10.5m) by Sunday, executives told Reuters news agency.
Meanwhile the movie's marketing plans will not be changed, despite the alleged plot to blow up US airliners.
Studio executives had considered scaling back advertising for the film in light of the news, but decided against it.
"The events of yesterday and today make this story even more poignant," said Don Harris, an executive vice president at film studio Paramount, "but I don't know whether it helps or hurts."
"How much more relevant could this movie be right now?" said Paul Dergarabedian of box office tracking service Exhibitor Relations.
"World Trade Center was never designed to be escapist entertainment anyway, so I'm not sure people will shy away from it given these real-life events," he added.
Starring Nicholas Cage, the film tells the true story of two police officers who were thought to have been the last people pulled from the Twin Towers.
Most reviews have been positive, with many praising the film's sensitivity.
Early audiences in New York were also positive.
"I was kind of sceptical but I really enjoyed it. It was done very tastefully," Maria Telemachos told BBC News.
Some survivors have criticised the film for being released so close to the fifth anniversary of the attacks.