A similar showdown is brewing between, on the one side, DreamWorks Animation and Paramount Pictures, which plan to release the animated “How to Train Your Dragon” in 3-D on March 26, and, on the other side, Warner Brothers. Warner has just decided to convert its sword-and-sandals fantasy “Clash of the Titans” to a 3-D format and release it on April 2. “How to Train Your Dragon” will have to make do with fewer 3-D seats, which sell for a $3 to $5 premium.

The 3-D bottleneck is likely to grow worse. Michael Lewis, the chief executive of RealD, which equips theaters that account for about 90 percent of 3D screens in the United States, said about 60 films were set for 3-D release over the next three years.

“As audiences experience more 3-D movies, scheduling challenges for theater owners and studios will naturally increase while there is a temporary shortfall of 3-D screens,” Chuck Viane, Disney’s president for distribution, said in a statement. Another Disney executive, who spoke on the condition of anonymity because he was not authorized to comment, said the studio did not see “Avatar” as a problem because early interest in “Alice in Wonderland” was quite strong.

“It will beautifully draft off of ‘Avatar,’ ” the executive said.

Fox, Imax and DreamWorks Animation declined to comment. Spokesmen for the Cinemark and AMC theater chains, which operate 3-D screens, did not return telephone calls. A spokesman for the Regal chain had no comment.

Imax long ago promised almost all of its 179 domestic and 82 foreign theaters to Disney for the opening of “Alice in Wonderland,” which stars Johnny Depp. At the time, few suspected that “Avatar” would still be racking up ticket sales that have made it the best-selling film in history, with more than $1.9 billion at the worldwide box office so far. In fact, the flagship Imax theaters in places like the AMC Loews Lincoln Square in Manhattan are still selling out weekend shows with no sign of a slowdown. More than 70 percent of ticket revenue for “Avatar” has come from 3-D.