The United States and Soviet Union began important and possibly final round of negotiations on a new strategic arms limitation treaty (SALT) here yesterday.

Secretary of State Cyrus Vance said afterward that conclusion of the pact is possible this year and announced that he and Soviet Foreign Minister Andrei Gromyko will meet President Carter at the White House Saturday to discuss the remaining issues.

Vance would give no details of the more than two-hour meeting of the U.S. Soviet Mission to the United Nations. He declined to say whether the few remaining differences had been narrowed.

He indicated that the Soviets gave their replies to U.S. proposals which were taken to Moscow earlier this month by Paul C. Warnke, director of the Arms Control and Disarmament Agency. The United States sent Warnke several weeks ahead of Gromyko's scheduled trip here in an effort to expedite a final agreement.

Standing outside the Soviet headquarters building after the meeting. Gromyko referred all questions to Vance except to say that he himself feels "wonderful." The veteran Soviet diplomat was taken ill and forced to leave the U.N. podium during an address to the General Assembly Tuesday. He appeared to be in good health yesterday.

Prospects for signing and Senate ratification of a new treaty, which has been under negotiation in its present form for more than a year, have brightened in recent weeks due to some lessening of the political tension between the two countries and the dramatic improvement in President Carter's domestic standing following the Egyptian-Israeli agreements at Camp David.

The few issues standing in the way of agreement, while strategically significant, have been less of a hurdle than the question of the determination of the two leaderships, especially that of the United States, to push ahead. In recent days, however, U.S. officials have been saying that the present moment is more favorable than in many months and expressed hope that Soviet accommodiation on the remaining issues will make an early resolution possible.

If the Soviets are in the mood to compromise, officials said, the SALT agreements may suddenly acquire a momentum of their own.

A timetable under ative discussion at the White House calls for agreement in principle to be reached this week or in the near future. Redrafting and technical details would be worked out within the next month or so, under this outline, and the first summit meeting of President Carter and Soviet President Leonid Brezhnev would be held this year - possibly shortly after the congressional elections in November - to finish unresolved points and give top-level blessings.

Such a timetable would leave the matter officially unresolved until after the elections, so that Senate candidates would not have to commit themselves on ratification before they have a chance to hear all the arguments. It would put the issue before the Senate early in 1979, well before the 1980 presidential political season.

All this depends, however, on the Soviet replies to the remaining issues, which were given to Vance and his team yesterday, and on Soviet and U.S. willingness to compromise in the meetings scheduled for this morning in New York and Saturday at the White House.

U.S. officials have been saying that they cannot afford to make many more concessions due to the apprehensions and political power of opponents of the SALT treaty in the Senate.

Under negotiation are a SALT II treaty to run until Dec. 31, 1935, a protocol covering particularly difficult points to run about three years, and a declaration of principles for a SALT III treaty to make great reductions in nuclear arsenals.

The most important remaining question involves restrictions on "new types" of land-based and submarine-based intercontinental ballistic missiles under the proposed SALT II treaty.

Both the United States and the Soviet Union would like certain exceptions from a ban on new missiles, to permit additions to their arsenals that are already planned. The problem is to draft the exceptions to accommodate both sides, without giving either one a relative advantage.

Other issues include a limit on the number of nuclear warheads that can be fired from a single land-based missile, proposed by the United States, and a limit on the number of cruise missiles that can be carried on aircraft, proposed by the Soviet Union.

Several technical problems such as the method of measuring the limited range of air-launched cruise missiles are unresolved.

A politically sensitive issue, which may be reserved for agreement at a summit meeting, is the U.S. request for Soviet restrictions on the deployment and refueling of the Soviet backfire bomber.

Another problem, although the U.S. insists it is not a negotiating issue, is the Pentagon plan to establish mobile land-based missiles that travel in secret between alternate firing positions in a nuclear "shell game" to baffle Soviet gunners in the mid-1980s. The Soviets have criticized this idea, but so far have not made their view a roadblock to a new SALT treaty.