Senators who had threatened to filibuster the $106 billion war supplemental if an amendment banning the release of photos of alleged detainee abuse was dropped said Wednesday they will hold fire now that Senate Majority Leader Harry Reid has pledged to allow another vote on the measure.

Reid's staff confirmed to FOX News on Wednesday that the leader is trying to get the measure, co-sponsored by Sens. Joe Lieberman, D-Conn, and Lindsey Graham, R-S.C., passed by unanimous consent.

The Graham-Lieberman bill was originally attached as an amendment to the emergency funding bill for the war in Afghanistan and draw down of troops in Iraq, but it was removed during House-Senate negotiations when anti-war House Democrats, whose votes were needed to pass the war measure, threatened to withdraw support for the supplemental.

It is unclear when the Senate could act.

Graham said he also spoke by phone with White House Chief of Staff Rahm Emanuel, and received assurances that President Obama would do all that is needed to ensure the photos are not released.

The American Civil Liberties Union has sued to have the photos released. The senator said he is convinced the president will sign an executive order to classify the photos, if need be, something the White House has not confirmed. 

Graham called on colleagues in the House to pull together a "discharge petition," a tactic unique to the House to force a measure onto the House floor for a vote.

Sen Jon Kyl, R-Ariz., a key supporter of the amendment, said a new vote in the Senate "would put a lot of pressure on the House to get something done."

FOX News' Trish Turner contributed to this report.