Secretary of State George P. Shultz will fly to Moscow next weekend at Soviet request to see Soviet leader Mikhail Gorbachev, the two nations announced yesterday as preparations for the U.S.-Soviet summit meeting went into high gear.

The announcement came as Shultz wound up a two-hour meeting with Soviet Foreign Minister Eduard Shevardnadze and as President Reagan ended three days of diplomacy here centering heavily on the Nov. 19-20 Geneva summit with the Soviet leader.

The invitation for Shultz to visit Moscow for summit planning came as a surprise and was known only shortly before Shevardnadze arrived in New York Wednesday night, State Department officials said. The officials said the request seemed to suggest a Soviet desire to improve chances for a successful Reagan-Gorbachev summit.

West German officials said Reagan agreed during Thursday's meeting with five allied leaders to brief them in Brussels following his two days of meetings with Gorbachev.

Two of the allied leaders, British Prime Minister Margaret Thatcher and West German Chancellor Helmut Kohl, said they came away from meetings here with Reagan with the understanding that the United States will present an arms-reduction "counterproposal" by the time of the Geneva summit.

Shultz, however, said Reagan has not decided about "an appropriate response" to the recent Soviet offer of a 50 percent cut in strategic offensive arms in return for a ban on strategic-defense programs such as his "Star Wars" plan. Other U.S. officials said the question of a U.S. counteroffer to the Soviets is in an early stage of discussion in the administration.

White House officials said Reagan has been reviewing various aspects of the Soviet offer in piecemeal fashion in a series of National Security Council meetings and cabling decisions to U.S. arms negotiators in Geneva as he makes them. The current round of the arms negotiations is scheduled to end next Friday.

The officials said Reagan is planning to make a major address on arms control and other summit topics within a week of his departure for the summit. This could be the occasion for announcements concerning U.S. arms positions.

Shultz, according to an administration official, hoped that Reagan would take the occasion of his address to the United Nations Thursday to discuss U.S. arms positions in detail. But Shultz was overruled by those in the administration who wanted to shift the focus of attention from arms control to regional issues, in hopes of placing the Soviets on the defensive, the official said.

Following a two-hour breakfast meeting with Shevardnadze this morning, Shultz said that some "genuine progress" has been made in U.S.-Soviet preparations for Geneva.

"At the same time I would have to say that there are major differences that need to be resolved and we hope that some of them at least may get resolved before the meeting in Geneva," Shultz added.

Shultz and Shevardnadze portrayed the secretary's trip to Moscow as a continuation of the presummit discussions that began in earnest with the meeting of the two foreign ministers at Helsinki, Finland, July 30, and continued with Shevardnadze's trip to New York and Washington a month ago and in his current visit.

Shultz plans to leave next Saturday on his way to Moscow, where his discussions are to take place Nov. 4-5. Shevardnadze described the Shultz visit as "the last stage" of preparation before the Geneva summit.

"Great hopes are pinned to the summit meeting by . . . all peoples in the world," Shevardnadze said. "It is in that spirit that we have our discussions with the secretary of state."

Senior administration officials who briefed reporters following the Shultz-Shevardnadze meeting said the two sides are exchanging memorandums that could be the basis for statements to be made by the leaders at the summit. They gave no details. Much of this morning's meeting, according to the briefers, was taken up with a detailed review of a variety of U.S.-Soviet negotiations, including those in the arms-control field and in bilateral fields such as cultural, consular and civil aviation.

Shevardnadze called in his U.N. address for U.S. positions that would facilitate "an agreement in principle" on arms issues at the summit. The briefers said Reagan and Gorbachev might be able to work out broad understandings at their meeting as "impulses" to guide their arms negotiators toward detailed agreements later.

The official briefers said Shevardnadze told Shultz this morning that Reagan's proposal in his U.N. address for negotiated solutions to five regional conflicts "will be studied" in Moscow. Shevardnadze did not say anything else about the proposal, the officials said. However, the Soviet news agency, Tass, denounced the Reagan proposal as a rehash of "bankrupt foreign policy directives" of the United States.

White House officials expressed some irritation at pressure from allied leaders for a quick U.S. response to the Soviet arms proposal. One official said the idea is being "blown out of all proportion" and that Reagan is "under no pressure" to offer a full-scale reply right away.

Vice President Bush, in an interview with the Associated Press, spoke in positive terms of the Soviet arms offers at Geneva, calling them "steps in the right direction" that might foreshadow an understanding on arms-control guidelines at next month's summit. Bush made clear that "we have some problems" with the Soviet offers but added that "until now there has been a distinct lack of specificity on the Soviet side and now they have come forward with something, and I would salute that."

Asked if he thought there is a "reasonable possibility" that Reagan and Gorbachev could agree on arms control guidelines to direct their negotiators toward later accords, Bush replied, "Yes, I do." At another point he described this as "an agenda" for the arms negotiators.

In an interview on NBC's "Today" program, White House chief of staff Donald T. Regan acknowledged that long-standing divisions still exist in the administration on arms-control topics.

"This is a very complicated subject," he said. "You hardly expect to get total agreement right off the bat. And the way you look at things has to differ from the point of view of what your job is. So that's a normal thing and a healthy thing because it gives the president choices. And that's what we want."

Regan added that "it might" send confusing signals abroad "but eventually they straighten out."