WASHINGTON, Sept. 19 — A move to give terrorism suspects the right to challenge their detentions in federal court fell short in the Senate today, even though it had majority support.

Fifty-six senators voted to cut off debate, and move forward to a vote on the bill itself, a step known as cloture. But under Senate rules, 60 votes are needed to invoke cloture.

Some supporters of the bill said they might bring it up again, although it was not clear just when. The cloture vote had been expected to fail, but the result did nothing to quell the debate over the proper balance between national security and personal liberty.

“The truth is that casting aside the time-honored protection of habeas corpus makes us more vulnerable as a nation because it leads us away from our core American values,” said Senator Patrick J. Leahy, Democrat of Vermont, a co-sponsor of the measure with Senators Arlen Specter, Republican of Pennsylvania, and Christopher J. Dodd, Democrat of Connecticut. Mr. Leahy is the chairman of the Senate Judiciary Committee and Mr. Specter the committee’s senior Republican; both are former prosecutors.