The United States and Soviet Union decided in talks here Friday to concentrate in the months ahead on resolving verification aspects of a strategic arms treaty in hopes of completing it in time for signing by President Reagan and Soviet leader Mikhail Gorbachev in Moscow next year.

The decision to make verification the highest priority item in the strategic arms (START) negotiations in Geneva, first disclosed by Soviet Foreign Minister Eduard Shevardnadze in a news conference here late Friday, was confirmed with additional details by U.S. officials yesterday.

Shevardnadze in his news conference noted that the problems of verification "will be much more complicated" and "much more numerous" in a strategic arms treaty than in the nearly complete pact banning medium-range and shorter-range missiles. He reported that he and Secretary of State George P. Shultz reached agreement in principle "that, at this stage, we shall focus on the problems of verification, that we shall study in depth all aspects of verification" concerning strategic arms.

A senior U.S. official who participated in the talks said several of the big issues still in the way of the proposed 50 percent cuts in strategic offensive arms probably require personal discussion and decision by Reagan and Gorbachev at their Washington summit due to begin Dec. 7.

These big issues include the makeup of the military forces that each side will be permitted to retain among its 6,000 nuclear warheads after the 50 percent cuts, and the sticky question of the relationship of space-defense restrictions to cuts in strategic offensive arms.

"Rather than wait for these to be resolved, we are telling the Geneva negotiators on START to begin working hard on verification issues" so this difficult group of questions will not be a time-consuming block to final agreement later, the U.S. official said.

Details of verification are among the final unresolved aspects of the prospective intermediate-range nuclear forces (INF) treaty that Reagan and Gorbachev have agreed to sign next month. U.S. sources said Shultz and Shevardnadze discussed the possibility of flying to Geneva before Dec. 7 to resolve any remaining problems that cannot be solved at lower levels.

The two foreign ministers also decided that Deputy Secretary of State John C. Whitehead and a Soviet official yet to be designated will meet to review human rights issues before the December summit, and that Undersecretary of State Michael H. Armacost and Deputy Foreign Minister Yuli Vorontsov will meet to review regional disputes such as the Persian Gulf, Afghanistan and Central America.

The human rights review is particularly welcome to the U.S. side because it was suggested by Shevardnadze. A White House official said Shevardnadze was also the first to bring up human rights in Friday's meeting with Reagan.

A personal letter from Gorbachev to Reagan, brought to Washington by Shevardnadze, focused on strategic arms and the desire that an accord can be signed when Reagan goes to Moscow for a return summit in the first half of 1988, according to an administration official who has read the letter.

As Reagan flew to Phoenix Friday afternoon to attend a memorial service for his wife's mother, Edith L. Davis, a senior White House official told reporters that "the newest element" in the developments of that day was "the Soviet interest in a summit in Moscow." He added that the Soviets "are clearly interested" in pursuing a strategic weapons pact to be signed there.

The senior White House official said Shevardnadze, in the meeting with the president, referred "two or three times" to a summit with Reagan in the Soviet Union next year. The official, who spoke to reporters on Air Force One, said Reagan would "stick to his bargain" to visit the Soviet Union next year even though Gorbachev is a year late in fulfilling his 1985 Geneva summit promise to come to the United States.

According to another administration official, who has read Gorbachev's letter, the Soviet leader reviewed the positions of the superpowers on strategic arms but did not make any new concessions. The document, typewritten in Russian and translated by the State Department, also included warm personal comments from the Soviet leader, the official said.

The letter offered no explanation for Gorbachev's apparent turnabout on a Washington summit this year, the official said. However, the official said the White House had been given several different explanations. One was that Gorbachev feared an assassination attempt in the United States. Another was that Gorbachev faced internal political resistance to a missile deal and to his economic policies and did not want to leave the Soviet Union now. The official said there had also been speculation that Gorbachev was trying to pressure Reagan into meeting in a third country.

Assistant Secretary of State Rozanne L. Ridgway said in a Cable News Network interview yesterday that despite evidence of Kremlin resistance to the leader's policies, "I don't think Gorbachev is in trouble."

Ridgway said Shevardnadze was "quite candid" in discussing some of Gorbachev's internal problems. Asked to assess Gorbachev's hold on power, Ridgway said, "I think it's a very firm grip. We still see him making changes in Politburo membership . . . . I don't think that's a sign of weakness."

Some U.S. arms control officials cautioned that there are hard decisions to be made on strategic weapons systems. They said that the Soviets seemed to make a political point that if the United States proposes tight constraints on land-based missiles, where the Soviets currently have an advantage, the Soviets will propose tight constraints on air-launched cruise missiles and submarine-launched ballistic missiles, where the United States has an advantage. They said they felt the Soviet approach was apparently not intended as a compromise that would move the negotiations forward. Staff writer R. Jeffrey Smith contributed to this report.