MOSCOW--The United States and Soviet Union yesterday gave their arms control negotiators one month to complete the key provisions of a new treaty to sharply reduce their strategic nuclear weapons.

The decision was taken as U.S. Secretary of State George P. Shultz wound up two days of talks in Moscow. He said negotiators in Geneva who have so far failed to make significant progress toward a 50 percent cut in long-range nuclear weapons were directed to report to him and Soviet Foreign Minister Eduard A. Shevardnadze in Washington March 22-23.

Shultz also told a news conference the Soviets indicated they would be more flexible in handling emigration applications, except for those from people who have had access to state secrets.

Shevardnadze confirmed "categorically" that only those with information the government considers important to national security would be barred from emigrating, according to Shultz.

Earlier today, as he opened talks with Shultz, Mikhail Gorbachev pledged to achieve peace in Afghanistan and to try reach a new nuclear arms agreement by spring.

Shultz and the Soviet Communist Party general secretary smiled broadly as they shook hands and sat down with their aides in opulent Catherine's Hall in the Kremlin.

At a picture-taking session, Gorbachev said the Soviets would "do our best to achieve peace in Afghanistan and to have a non-aligned, neutral Afghanistan which would have good relations with its neighors, with the United States and with the Soviet Union."

At the news conference, Shultz said he did not have the "slightest doubt" that the Soviet Union would leave Afghanistan. But Shultz, who came here saying he would seek a specific timetable, gave no evidence he had received one.

An estimated 115,000 Soviet troops have been in Afghanistan since December 1979, backing a pro Moscow government at war with U.S.-armed Moslem guerrillas.

Gorbachev has promised to begin a withdrawal on May 15 if the Kabul government and Pakistan can agree on terms of a settlement by March 15.

Shultz, who arrived in Moscow on Sunday, met until 1:30 a.m. yesterday with Shevardnadze, then held talks with Premier Nikolai I. Ryzhkov before meeting Gorbachev.

After the talks, Shultz did not say whether the Soviets agreed to support the seven-month U.S. effort in the United Nations to impose a worldwide arms embargo against Iran for refusing to comply with a U.N.-ordered cease-fire in the Iran Iraq war.

Shultz also vehemently denied that he sought Soviet backing for his Middle East peace initiative.

"I didn't come here with my hat in hand looking for support," he said.

He said the parties in the region, Arabs and Israelis, would determine whether his trip to the Middle East later this week will succeed.

The secretary of state has questioned whether the Soviet Union can play a bigger role in that region because of its human rights record and its lack of relations with Israel.

On nuclear arms, Gorbachev said "there is still a chance" of an agreement to reduce by half U.S. and Soviet long-range nuclear weapons by the spring. The idea would be to have the pact ready for him and President Reagan to sign at a Moscow summit.

Gorbachev and Reagan signed an agreement in Washington Dec. 8 to eliminate their intermediate-range missiles, which have a range of about 300 to 3000 miles. The current negotiations in Geneva concern those with a range above 3000 miles.

The Geneva talks have been held up because of disagreements over the future of Reagan's "Star Wars" antimissile program and how to verify any new arms treaty.

Shultz said the negotiators would have until his meeting in Washington with. Shevardnadze to put together three draft documents dealing with verification procedures, ways to eliminate or convert the weapons and methods to help inspectors observe treaty compliance.

On Sunday, Shultz quizzed Andrei D. Sakharov about human rights, arms control and Soviet reforms and met with a group of Jewish refuseniks to underscore U.S. concern for human rights in the Soviet Union.

Sakharov, who won the 1975 Nobel Peace Prize for his efforts to protect human rights, met with reporters after seeing Shultz.

Sakharov said the Soviet Union has not yet made enough progress to merit holding an international human rights conference.