Starting with next month's trip to Moscow by Secretary of State George P. Shultz, the Reagan administration will mount a major drive to negotiate and sign a U.S.-Soviet treaty sharply reducing strategic offensive arms by spring, senior State Department officials said yesterday.

The officials, analyzing the results of last week's meetings with Soviet Foreign Minister Eduard Shevardnadze, said a strategic arms pact in time for Senate ratification during the Reagan administration now seems a possibility, though they also cautioned that imposing hurdles remain to be overcome in a period of only a few months.

President Reagan referred to perhaps the highest hurdle in his weekly radio speech yesterday, saying that while the two nations agreed last week "to forge ahead" toward halving their strategic, or long-range, arms arsenals, "I made it clear to the Soviet foreign minister that I will not sacrifice our SDI {Strategic Defense Initiative} program." The Soviet Union continues to insist that strategic defense programs be curbed as a condition for large-scale cutbacks in strategic offensive arms, which include intercontinental ballistic missiles (ICBMs).

Recent headlines concerned the highly publicized "agreement in principle" to conclude a treaty eliminating medium-range and shorter-range nuclear missiles and the announcement that a summit meeting of Reagan and Soviet leader Mikhail Gorbachev will be held here this fall. Officials said significant accomplishments were also achieved in other areas, including a 13-point "work program" of bilateral negotiations in coming months and an improved U.S.-Soviet dialogue on human-rights questions.

A principal basis for optimism rests on a more realistic, businesslike and accommodating Soviet attitude, which U.S. officials said was evident in the talks with Shevardnadze and his aides on a broad range of topics here last week. "It was the best-ever meeting" with Soviet officials in this administration, according to a State Department official who said the new flexibility suggests that U.S.-Soviet relations have stabilized after nearly a decade of trouble and uncertainty.

Among the factors cited by administration officials yesterday to explain the success of the meetings were: Gorbachev's need for a pause or permanent reduction in superpower rivalry and his desire for an arms treaty; the placement in high government and Communist Party posts of a pragmatic "American-affairs mafia" headed by former ambassador to the United States Anatoliy Dobrynin, and Shevardnadze's positive relations with Shultz, as well as his growing authority and confidence. Shevardnadze, former Communist Party chief in Soviet Georgia, was an unexpected choice in 1985 to succeed Andrei Gromyko, foreign minister since 1957.

Bolstering this, U.S. officials say, was the familiarity and mutual respect of Soviet and American diplomats and other negotiators who have sat down with one another many times since Gorbachev came to power in March 1985, and, not least, Reagan's desire for achievements in U.S.-Soviet relations as a capstone of his presidency.

In the field of bilateral relations, U.S. and Soviet experts at last week's talks worked out an extensive "work program" for negotiations in coming months that promises to pay off in future agreements.

Among items on the agenda, according to State Department officials, are: exploratory talks next month on a revived U.S.-Soviet transportation technology agreement; talks by mid-November on ways to resurrect a dormant accord to conduct oceanic experiments; early completion of a fisheries accord that would provide U.S. access to the Soviet offshore economic zone; new talks in October or November on delineating the U.S.-Soviet boundary in the Bering Sea and, in the same time period, on uses of seabeds.

Also, new talks on the future of the U.S.-Soviet long-term grain agreement by early next year; completion of talks on maritime search and rescue cooperation; discussions of enhanced cooperation in maritime and airport security; bilateral discussions of the ozone-depletion problem; discussions of scientific cooperation in agriculture; a push toward new accords in international nuclear fusion experiments; a renewed commitment to expanding people-to-people exchanges, and further discussions next March on bilateral issues across the board.

The human-rights discussions featured less tangible agreements but both Shultz and Shevardnadze publicly expressed satisfaction with them. This is a major shift from the days when the Soviets either flatly refused to discuss human-rights cases and issues on grounds that they are internal matters or insisted that discussions proceed without public notice.

Shevardnadze justified his satisfaction by noting that the human-rights talks are now "a two-way street." According to Assistant Secretary of State Richard Schifter, the Soviets raised issues of the death penalty here for offenses by persons under 18 years old and severe U.S. punishment for some antiwar protesters.

Schifter said he responded that the issue of capital punishment for minors is before the U.S. Supreme Court and offered to obtain the briefs for the Soviet officials. On the other issue, Schifter said the Soviets referred to antiwar protesters who received 18-year prison terms (later reduced to 12 years) for attacking a Minuteman missile silo with a jackhammer. "I asked what punishment might be given in the Soviet Union for attacking a missile site," Schifter said.

Having justified human rights as a "two-way" issue, Schifter reported, Moscow's team discussed in satisfying detail their plans for changes in the Soviet legal system and its application to dissidents, would-be emigrants and others, and agreed to a continuing point of contact to discuss individual cases.

Large-scale cuts in strategic offensive arms have long been described as a top priority by the administration, such as the 50 percent reductions endorsed in principle by Reagan and Gorbachev as far back as their November 1985 talks in Geneva. What is different now is the U.S.-Soviet agreement here last week to make an "intensive effort" to achieve this goal and, at least as important, the increasingly specific U.S. planning to make such a serious push in the strategic arms arena in coming weeks.

Two new messages from Moscow encourage those within the administration who believe there is a real chance for an early strategic arms accord. One is Gorbachev's declaration in his Pravda and Izvestia article last Thursday that a strategic arms treaty "could become a reality as early as in the first half of the next year," given mutual efforts. The other is the seemingly reduced Soviet requirement for U.S. curbs on space defense, outlined by Gorbachev in the article and Shevardnadze in the Washington talks as "the strict observance of the {1972} Antiballistic Missile Treaty."

It remains to be seen how far the Soviets will retreat from binding space-defense curbs or how far Reagan will be willing to move toward SDI limits in exchange for a tempting strategic arms reduction package. If the Soviets agree to major accommodations on strategic offensive forces, Reagan may well be faced with a slow-motion version of last October's Reykjavik summit, in which he was forced by Gorbachev to choose between massive offensive cuts and an unrestrained SDI program. Next time, though, the proposed curbs on SDI could be more modest.

State Department officials said Shultz's forthcoming trip to Moscow, initiated by the Soviets and likely to take place the third week in October, could be the occasion for seeking high-level political decisions to resolve some knotty strategic arms problems. If this can be done, further progress might be made when Gorbachev comes to Washington for the summit, probably in late November, with the aim of having a strategic arms treaty ready to be signed on a Reagan "return summit" trip to Moscow next March.

Soundings with key senators by the State Department suggest it is at least theoretically possible to ratify a strategic arms accord before Reagan leaves office if the pact is signed by March. A U.S. official intimately familiar with the strategic arms negotiations in Geneva said it is "technically and politically possible" to obtain a treaty by spring, though it would take prodigious efforts to do so.