WASHINGTON — The Senate moved closer on Monday to approving a new arms control treaty with Russia over the opposition of Republican leaders as lawmakers worked on a side deal to assure skeptics that the arms pact would not inhibit American plans to build missile defense systems.

A Republican senator announced that he would vote for the treaty and two others said they were leaning toward it after a closed-door session on classified aspects of the pact. At the same time, Senator John McCain, Republican of Arizona, produced separate legislation that could reassure fellow Republicans worried about the treaty’s impact on missile defense.

By the end of another tumultuous day, treaty backers said they could count more than the two-thirds majority required for approval in votes that could begin as early as Tuesday. The Senate mustered as many as 64 votes in defeating Republican amendments on Monday, just two short of what supporters need for final approval, and three senators who supported one of the amendments have already said they will vote for the treaty in the end.

The momentum building for the treaty came despite the announcements of the two top Senate Republican leaders, Mitch McConnell of Kentucky and Jon Kyl of Arizona, that they will vote against the treaty, known as New Start. Treaty supporters pressured wavering Republicans on Monday with an appeal by Adm. Mike Mullen, chairman of the Joint Chiefs of Staff and the nation’s top military officer, to approve the agreement.