In an unusual political gambit, three senators who are expected to support a new strategic arms limitation agreement with the Soviet Union have written to President Carter urging him to stiffen that agreement before submitting it to the Senate.

The three senators, all Democratic members of the Research and Development Subcommittee of the Armed services Committee, gave Carter a list of six points on which, they said, the new agreement should be firmed up "to strengthen the agreement and to broaden support for ratification."

The letter was signed by Sens. Thomas J. McIntyre (D-N.H.) John C. Culver (D-Iowa) and Dale Bumpers (D-Ark.) and was delivered to Carter Tuesday. Culver released it yesterday.

The fact that such a letter could be sent now - when negotiations are still going on with the Soviets on the new agreement - suggests the unprecedented political situation that has developed around this round of strategic arms limitation talks (SALT).

Even before final agreements are reached - and officials estimate that they won't be completed until spring - likely supporters and foes are mobilizing in the Senate for the coming battle over approval.

This has been made possible by a succession of leaks on the new agreements which has allowed an unprecedented degree of public comment on an ongoing set of negotiations with the Soviet Union. There have been leaks on previous SALT negotiations, but never so detailed, and never with such an attentive audience looking on.

The administration had already been counting on McIntyre, Culver and Bumpers to support the new SALT agreements, probably correctly, according to Senate sources. But - as an administration official noted yesterday - these three senators might be more effective in the coming SALT debate if they can now establish that they are not patsies for the President's position.

In their letter released yesterday, the senators told Carter that a new agreement should include "as stringent limits as possible" on improvements in Soviet rocket technology, and a series of specific points that would presumably appeal to other Senators who are now unsure how they will vote.

Those include: a clear understanding that if the range of U.S. cruise missiles (unmanned drones that can carry atomic weapons) is limited to a certain number of miles that the Soviets understand the need to allow a greater practical range so the cruise missile can follow an indirect flight path to its target; some assurance that the Soviets will not put an intercontinental missile in mobile, land-based launchers that are usually used for medium-range missiles targeted at Europe; and explicit assurance that the Soviet Union will complete dismantling the weapons that it will have to give up under the new agreements within three years of their signing.

A Senate aide critical of the new agreements said yesterday that the senators' letter "doesn't ask any of the hard questions," but only asks for things they know the United States is likely to get in the ongoing negotiations.

But a spokesman in McIntyre's office insisted that the senator was seriously concerned about the specific issues raised with Carter, most of which have come up during hearings before the research and development subcommittee he heads. Assurances on these points, the spokesman said, would make it easier for McIntyre to urge approval of the new agreement.