The United States and the Soviet Union yesterday agreed to future negotiations aimed at a second treaty on strategic nuclear arms, even as they failed to reach key agreements needed to sign a first strategic arms accord this year.

A joint statement signed by President Bush and President Mikhail Gorbachev at the White House called for the new negotiations to begin "at the earliest practical date" after the remaining arms disputes are settled and an initial treaty is signed.

U.S. officials said the pledge on new negotiations was designed in part to preempt expected criticism of the initial accord, known as START I, which they said will not meet its advertised goal of reducing existing arsenals by 50 percent.

"In the new negotiations {on START II}, the two sides agree to place emphasis on removing incentives for a nuclear first strike" and on moving to an arsenal of less-vulnerable weapons that are not suited for use in such a preemptive strike, the statement said. START I does not include special constraints on missiles that carry multiple warheads, which are the weapons best-suited for launching a first strike.

Several officials, who asked not to be identified, said they hope the pledge would please legislators who have advocated more sweeping nuclear arms reductions than START I will deliver, including limitations of missiles carrying multiple nuclear warheads. The statement was developed after an intense last-minute negotiating session at the State Department yesterday afternoon involving Secretary of State James A. Baker III and Soviet Foreign Minister Eduard Shevardnadze.

U.S. officials said the two sides were unable to resolve their disputes over START I limitations on the Soviet Backfire bomber or the Soviet SS-18 missile. They also did not agree on monitoring requirements for mobile, land-based missiles or measures to prevent future circumvention of the accord.

Baker said the negotiators had "made tangible progress" on these issues, and reaffirmed their desire to complete work as quickly as possible. He and others noted that the two sides had settled one major dispute, agreeing on a limitation of 1,100 warheads on mobile, land-based missiles in START I. That figure was a compromise between a Soviet proposal for 1,200 such weapons and a U.S. proposal of 800. The Soviets already have roughly 470 warheads on mobile, land-based missiles; the United States has none.

In talks about separate negotiations on limiting conventional forces in Europe, the two sides made headway by agreeing to some limitations on tanks and armored personnel carriers. But there was "no particular convergence" on the key issue of limiting tactical aircraft, a senior official said.

He said there remained "fairly considerable work" ahead on "some very tough, complicated details" of the East-West conventional arms accord now being negotiated in Vienna, which Bush and Gorbachev pledged yesterday to complete this year and sign at a summit meeting of European leaders.

U.S. officials said the new agreement on future strategic arms negotiations did not reflect as precise a commitment to reductions in large, multiple-warhead missiles as the Bush administration initially sought. But it also did not reflect Soviet desires for dramatic overall cuts in such weapons.

"We chose fuzzy words that will allow both sides to say they got most of what they wanted," a senior official said.

The Bush administration until recently was reluctant to commit to prompt negotiations on START II, but shifted under pressure from the Soviets and from liberals who said that eight years of superpower negotiations on START I had accomplished little. Both sides will be able to continue their current strategic modernization under START I, and arsenals on each side will shrink by only 10 to 30 percent.

The administration has also been criticized by conservatives for not doing enough to constrain the Soviet SS-18, a 10-warhead weapon that is believed capable of destroying U.S. missile silos. Under START I, the SS-18 missile force will be halved, but conservatives have said that the remaining missiles -- a modernized version of the SS-18 -- will have greater military effectiveness than those being eliminated.

THE CIVIL ACCORDS IN BRIEF

Key provisions of six civil agreements to emerge from the summit:

Cultural Exchange Agreement

Nondiplomatic, nonprofit cultural centers will be opened in Washington and Moscow to operate libraries, sponsor seminars, films and performances and provide student counseling and language instruction. According to a memorandum of understanding, circulation of the magazines America in the Soviet Union and Soviet Life in the United States will be increased to 250,000 copies in 1991. Existing scholarly and academic exchanges will increase by 250 students bilaterally in academic year 1991-92. Exchanges will increase to 1,500 bilaterally by 1995-96, depending on financial constraints.

Environmental Agreement

Both countries will help establish a natural preserve, the Beringian Heritage International Park, on the Bering Sea. The agreement also calls for closer cooperation by environmental organizations in the United States and Soviet Union.

Expanded Civil Aviation Agreement Calls on both countries to double the capacity of passenger and cargo flights to the equivalent of 15 Boeing 727 flights per week. (A modern 727-200 carries 189 passengers.) By 1992, the total number of flights would increase to 58 per week. Allows Soviet airlines to retain unrestricted rights to sell tickets in the United States; 8.75 percent of the space on U.S. airlines flying out of the Soviet Union could be purchased with rubles by Soviet citizens, who will buy these tickets through Aeroflot. The Soviet airline will reimburse the American carriers. This will give U.S. carriers access to Soviet travelers who cannot purchase tickets with hard currency. The agreement also says that:

Seven additional U.S. airlines will be permitted to fly between the two countries, and a second Soviet airline will be allowed to join the competition if one is formed as expected.

U.S. airlines could increase service to Moscow and Leningrad, while Soviet airlines could increase flights to Washington and New York. In addition, four U.S. cities, Anchorage, Chicago, San Francisco and Miami, could be served. In the Soviet Union, the cities of Kiev, Minsk, Magadan, Khabarovsk, Tbilisi and Riga would be added as service points.

100 charter flights a year would be allowed to travel between the two countries on transatlantic routes.

Grain Sales Agreement

Requires the Soviet Union to purchase at least 10 million metric tons of U.S. grain per year over the next five years -- 1 million tons more than is now required.

Maritime Transportation Agreement Commits both countries to eliminating discriminatory treatment of cargo and provides for other improvements in maritime trade and cargo-handling between the two countries. Also settles long-standing boundary disputes about the Alaskan coast.

Ocean Studies Agreement Provides for a broad range of joint oceanographic research, the use of port facilities in both countries and scientific exchanges. Also calls for joint studies to be published openly in both countries.

Customs Agreement Provides for mutual assistance and cooperation between customs services of the United States and Soviet Union deterring and detecting narcotics trafficking. Creates framework for cooperation in customs law enforcement assistance, export control and commercial fraud.

Trade Agreement Paves the way for the eventual lowering of tariffs on Soviet goods.

Atomic Energy Agreement Provides for substantial cooperation in atomic energy research.