Bipartisan groups of members of Congress cautioned President Reagan in separate letters yesterday that they may withhold support for the new MX missile unless he undertakes more clear-cut and immediate initiatives to control nuclear arms.

Meeting with reporters after co-authoring one of the letters, Senate Foreign Relations Committee Chairman Charles H. Percy (R-Ill.) said he believes that Reagan supports arms control.

But, Percy said, "I have no doubt that there are certain people around him, in the National Security Council and the Defense Department, who will do anything to prevent arms control. These are the guys I am out to get." Percy mentioned no names.

Rep. Albert Gore Jr. (D-Tenn.), who co-authored the other letter, said later that "there is a lot of concern" about the administration's enthusiastic endorsement of a special presidential commission's recent recommendation to deploy 100 MX missiles and its apparent lower level of interest in other panel recommendations on arms control and development of a small, single-warhead missile to succeed the 10-warhead MX.

Both groups also urged Reagan to establish a bipartisan commission "to advise you on implementing" the arms-control recommendations of the presidential commission on the MX and other issues that was headed by retired Air Force Lt. Gen. Brent Scowcroft.

Yesterday's letter from Percy and Sens. Sam Nunn (D-Ga.) and William S. Cohen (R-Maine) said that such a commission would "underscore to our allies and adversaries the continuity of U.S. arms-control policy beyond any one administration."

Senate aides said later that the Soviet Union's incentive to bargain has been reduced by the inability of past administrations to obtain ratification of agreements on missiles or nuclear testing worked out with Moscow but then disapproved by subsequent administrations.

In their letter, the senators said, "We are concerned that the administration has not responded more fully to the arms-control recommendations" of the Scowcroft panel.

Specifically, they asked Reagan to modify the existing U.S. proposal at the Geneva arms talks quickly to bring it in line with the commission's recommendation that both sides measure their forces in numbers of atomic warheads rather than missile launchers.

They stressed that, "without effective arms control," the idea of putting MXs in existing and vulnerable Minuteman silos or even of building the new small missile does not make much sense.

"We believe that explorations should begin at once to determine whether there is any reasonable prospect of agreement with the Soviets" to the kind of more stable nuclear forces on both sides advocated by the commission, they said.

This would mean an ultimate move away from big, multiple-warhead missiles toward the smaller, more secure and less threatening single-warhead versions.

The senators called for "an immediate start" on the small missile and endorsed an earlier Nunn-Cohen proposal under which the superpowers would eliminate two old atomic warheads for each new one added.

The lawmakers warned Reagan that "before we reach a decision on . . . opening the production line for the MX missile, we would like an expression of your opinion on the approach we have outlined."

Both groups also said the number of MX missiles ultimately deployed should be contingent on arms-control developments.

White House officials said yesterday that there is "no doubt" that the administration views the Scowcroft commission's recommendations "as a package" and that the small missile is "very integral to it." A study is already under way on revising the U.S. proposal at Geneva, they added.

The House letter was authored by Gore, Les Aspin (D-Wis.) and Norman D. Dicks (D-Wash.), and was signed by several other Democrats and at least one Republican.