Senate leaders worked behind the scenes yesterday in hopes of averting a clash on the Senate floor over a proposal to send the Pentagon's $180.3 billion procurement bill back to committee for a rewrite.

Sens. Carl Levin (D-Mich.) and John G. Tower (R-Tex.) were on the verge of colliding on that issue, with Levin asserting that President Reagan's willingness to settle for a lesser figure for defense demanded that the Armed Services Committee redo the bill now on the floor.

Tower, chairman of the Armed Services Committee, opposes any such derailing and wants to see the bill passed intact before the Senate Budget Committee sets a ceiling on how much is needed for national defense. Critics complain that Tower is trying to put the cart before the horse in insisting on this procedure.

During a meeting of the Senate Democratic Caucus yesterday, it was agreed that Sen. John C. Stennis (D-Miss.), formerly chairman and now ranking minority member of the committee, should approach Tower about going ahead with the debate and amendments to the procurement bill but holding off the final vote on passage until the Budget Committee has set a target ceiling.

If Tower is unwilling to do this, sources said, Levin and his allies plan to go ahead with their original plan to ask the Senate to recommit the measure to Armed Services for a rewrite.

While efforts to work out a compromise proceeded in private, Tower and Sen. Arlen Specter (R-Pa.) argued on the floor over "sense-of-the-Senate" resolutions designed to underscore the need for Reagan and Soviet President Leonid Brezhnev to hold a summit meeting. The compromise wording said such a meeting was urgently needed, steering away from who should invite whom.