President Reagan called upon the Soviet Union today to set a timetable for withdrawing troops from Afghanistan and ending the "six years of utter hell" for that country.

In his weekly radio speech, Reagan denounced the "brutal onslaught" and "daily atrocities" he said the Soviets were committing on the Afghan people.

The president repeated an offer he made in his speech to the United Nations last October that the United States was willing to serve as "guarantor of a comprehensive Afghan settlement." But he said that such a settlement would have to include withdrawal of all foreign troops, "genuine independence" for Afghanistan and resettlement of the refugees who have fled the country because of the war.

Reagan's speech today, following a similarly worded written statement by the president Friday marking the sixth anniversary of the invasion, appeared to be an effort to maintain pressure on the Soviets to seek a political settlement in Afghanistan.

Such a settlement seemed a possibility to U.S. diplomats after the mid-November summit meeting between Reagan and Soviet leader Mikhail Gorbachev. Soviet statements on Afghanistan at that meeting appeared to offer hope for a settlement, and Gorbachev said at a reception this week that he looked forward to "essential progress" on regional issues, including Afghanistan, in 1986.

In his remarks Friday, Gorbachev, according to a translation by the Tass news agnecy, used the phrase "around Afghanistan" when referring to the need for political settlements. Some U.S. officials interpret this to mean Gorbachev was talking about the need to stop aid to rebels flowing into Afghanistan through Pakistan and other countries, rather than a call for negotiated settlement inside the country. The Soviets have signaled no change in overall policy in the Afghan conflict.

The military situation is unchanged in Afghanistan, and the Reagan administration is skeptical that the Soviets will match their words with deeds.

"We have seen in the Soviet statements some hope of progress," White House spokesman Larry Speakes said today. "The president is anxiously awaiting some demonstration of this intention from the Soviet Union."

Reagan, meanwhile, has decided to keep the spotlight on the invasion while waiting to see what the Soviets will do. He said in his radio address today that the Soviets understand that "the battle for Afghanistan has shifted from the mountains of Afghanistan itself to the wider field of world opinion."

"So it is that the Soviets are prolonging the war and blacking out news about the daily atrocities which they're committing," Reagan said. "They're waiting for world attention to slip, for our outrage to wane."

Reagan said that the United States would "place no barriers" on a Soviet withdrawal and observed that the sixth round of U.N. negotiations aimed at achieving a settlement had ended without result.

"If the Soviets want progress, they must simply put forward a timetable for the withdrawal of their forces from Afghanistan and for the restoration of the rights of the Afghan people," Reagan said.

In mid-December, the Soviet-backed Afghan government in Kabul hinted at a schedule for Soviet withdrawal, an overture that is believed to have required Moscow's approval. Like other suggestions, it has yet to produce results.

After delivering his speech, Reagan taped a message that will be delivered to Moscow for use on Soviet television at 9 p.m. New Year's Day. Speakes said the message continued "the spirit of Geneva" and emphasized the need to work on "areas of agreement" in 1986. He declined to say whether Reagan mentioned Afghanistan in the statement, which the Soviets have promised to use in its entirety.

A message from Gorbachev to the American people will be made available to U.S. networks for use at 1 p.m. New Year's Day.