Secretary of State Cyrus R. Vance began taking soundings on Capitol Hill yesterday for a nuclear arms control compromise with the Soviet Union that could include restrictions on developing American long-range cruise missiles.

A possible trade-off with the Russians would permit continued U.S. development of air-launched, long-range cruise missiles but would put a three-year moratorium on testing the sea-launched and ground-launched versions.

This possibility was among the formulas outlined by Vance to Soviet foreign minister Andrei A. Gromyko in the nuclear strategic arms limitation talks (SALT) in Geneva last week, according to American sources.

Administration officials refuse to confirm or deny any details of the secret talks. Sen Henry M. Jackson (D-Wash.), a champion of cruise missiles and chairman of the Senate Armed Services Arms Control Subcommittee, is expected to question Vance closely Thursday on the cruise missile discussions. Administration officials privately concede this may be the first critical test in Congress of U.S. strategy in the ongoing SALT negotiations.

Vance was questioned only lightly and briefly at a hearing yesterday before the House International Relations Committee on his three days of negotiations with Gromyko which produced agreement on a negotiating format.

The hearing was delayed by vote on the House floor and before it was quickly closed to the public at Vance's request, Vance said: "I would emphasize that a number of difficult and important issues remain before us on which we are not agreed with the Soviet Union." He added, "We have a lot of ground to cover."

Vance is due to testify in closed session today before the Senate Foreign Relations Committee, before facing the Jackson subcommittee the next day.

Until now, President Carter has enjoyed widespread support among Senate nuclear hard liners and moderates for his original nuclear arms proposals, which were flatly rejected by the Soviet Union in March. Carter has made special overtures to retain support of Jackson, who wields strong influence over the two-thirds Senate vote that is required to approve a SALT treaty.

State Department spokesman Hodding Carter III yesterday sidestepped questions on whether the United States did discuss in Geneva "a moratorium" on developing cruise missing.

"It is not useful for us to comment on any possible aspects of the overall framework" of a SALT agreement, Carter said, because "all details in the package are inter-related."

He said the administration will stand on the position expressed by Vance at the end of last week's talks with Gromyko, that there is no agreement yet on all the components of a three-part "framework for negotiations" that was decided upon in Geneva.

That framework includes a treaty to run until 1985, generally based on the nuclear force levels set a Vladi-departure from President Carter's original calls for deferring the cruise missile and Backfire issues to talks on "substantial reductions" in arms levels. To accept any limits on these missiles, critics claim, would embed the limitation into SALT III negotiations on "deep cuts" in nuclear arm levels, vostok in 1974, of 2,400 strategic missiles and bombers for each side; a three-year protocol to deal with such disputed issues as cruise missiles and Soviet Backfire bombers, and a statement of principles for subsequent negotiations (SALT III) on greater cuts in arms levels, the American priority.

One report, by Aviation Week and Space Technology, said that in Geneva the United States suggested a moratorium on cruise missile deployment until SALT III in exchange for possible restrictions on the Soviet Backfire, and "some reductions" in the Vladivostok strategic force levels.

Other sources said that a formula suggested by the United States would permit continued development of the American 1,500-mile-range, air-launched cruise missile, but curb testing of long-range, sea-launched and the ground-launched cruise missiles.

The Russians originally sought a 600-kilometer range limit on all these missiles, long enough to protect their shorter range cruise missiles. The Carter administration has sought a 2,500-kilometer (1,550-mile) range limit on all types of cruise missiles. The Russians have indicated they might agree to that range for only air-launched cruise missiles.

Cruise missiles are similar to a low-flying pilotless aircraft, with exceptional accuracy. The United States has a major technological lead in developing long-range versions. The Russians are particularly determined to restrict the long-range sea-launched and ground-launched versions.

Advocates of a moratorium on testing long-range sea and ground versions argue that if they are limited for three years to tests of 600 kilometers (373 miles), as the Russians insist, considerable American development would still be possible.

Opponents charge that making any concession on cruise missile deployment would be a major, unacceptable