Top-level U.S. and Soviet officials reportedly made some progress here on the second day of talks about possible new nuclear arms limitation agreements. They scheduled a third day of discussions Friday that informats say is crucial to the current round of negotiations.

The participants appeared to have reached a point in their bargaining in which further instructions and decisions were required overnight from the White House and the Kremlin.

Secrecy about the talks in the Soviet mission here remains tight. There were indications however, that delegations led by U.S. Secretary of State Vance and Soviet Foreign Minister Andrei Gromyko were making some progress toward at least laying the groundwork for a compromise in the statemated positions of the two superpowers.

One official cautioned that everything depends on Friday's meeting.

State Department spokesman Hodding Carter declined to characterize the talks in anything but general terms.

"What we have had is a very thought review," he said. He cautioned that it was premature to comment further.

He did tell reported earlier, however, "the fact that we have had over five hours worth of talks and have more scheduled leaves the implication that we are having a full, businesslike, good-faith negotiations."

He said the two delegations would take a pause from SALT this afternoon to allow delegates to reflect on those exchanges, while the conversation shifted temporarily to the Middle East. Carter also said the arms talks would probably last until saturday, another sign that some movement was taking place.

Earlier in the day, U.N. Secretary-General Kurt Waldheim left a different picture of the U.S. Soviet nuclear arms talks.

At a news conference, Waldheim said "I think we cannot expect a quick solution on a new agreement. It is evident that there are deep differences between the sides that have not been brdiged to my knowledge since Moscow and the meetings thus far."

His reference to Moscow related to the trip there by Vance in March during which the Kremlin brusquely rejected the first two arms limitation proposals of the new Carter administration.

Although Waldheim does not sit in on the talks here, he had a two-hour breakfast meeting today with Vance following yesterday's round of talks.

"Secretary Vance was good enough to keep me informed on the main aspects of the problem" Waldheim told reporters.

Waldheim's remarks appeared to ruffle some U.S. officials. Asked about them later, Carter told reporters that Waldheim made it clear he was speaking for himself and not Vance and that the U.N. official "simply does not know what's going on inside the room."

Emerging from an hour and three-quarter talk this evening at the U.S. delegation's headquarters, Gromyko told reporters that "both sides agree that the most expedient forum for the consideration of the Middle East question is the Geneva conference."

Vance and Gromyko described the situation in the Middle East as dangerous, but Vance rejected the idea that this was because of the victory of the conservative Likud group in Tuesday's Israeli election.

Spokesman Carter said later that the Middle East talks were not conducted "in an atmosphere of crisis or sudden re-evaluation."

The prospect for a compromise in the U.S. Soviet positions on arms limitations, which was also hinted at by waldheim today, has generally centered on combining elements of the most recent U.S. and Soviet proposals.

The most likely propsect, however, appears to be one that at the outset would be closer to the views of Soviet Communist Party chairman Leonid Brezhnev than to the plan fovored by President Carter.

U.S. officials here have been stressing privately that if a compromise is worked out that is closer to the current Soviet position at least on the surface, it will contain a commitment to begin work immediately toward a third major SALT agreement. This accord would strive for the type of limitations President Carter is seeking in his comprehensive plan.

In March, United States presented two proposals to Moscow.

One was a comprehensive plan calling for cuts in the levels of nuclear-tipped missiles, bombers and multiple-warhead missiles in each arsenal, plus an important freeze on development of new missiles and modernization of older ones. It also conained some limits on the controversial new U.S. cruise missiles and the Soviet Backfire bomber.

The second so-called "fallback" U.S. position was a simple ratification of the 1974 Vladivostok agreement between former President Ford and Brezhnev that was never formalized and a deferral of the cruise missile-Backfire question.

The Soviets proposed the Vladivotok levels plus limits on cruise missiles.

Since then, the Soviets have been unofficially reported as willing to discuss some relatively minor reductions in existing weapons, below the Vladivostok levels, as a stop toward the U.S. position. The secrecy here and in Washington on the question of how to work out the cruise missile dilemma makes it very difficult to determine if a real bargain can be struck.