Three times in the past week Soviet leader Mikhail Gorbachev ushered private U.S. citizens into his Kremlin office, on each occasion stressing different points of interest between the United States and the Soviet Union -- from sports to space weapons to a moratorium on nuclear testing.

After conveying a series of overtures through the United States' European allies, the Soviet leadership is making direct approaches to influential American citizens to emphasize a desire to build a more constructive relationship with Washington.

For domestic as well as foreign policy reasons, the U.S.-Soviet dialogue is starting again. Both sides are feeling the pressure to set the dates and terms of the second summit meeting between President Reagan and Gorbachev, to be held this year in Washington, according to their agreement last November.

But as the ice between Washington and Moscow breaks, lasting disputes are laid bare. The differences between the two sides on Reagan's Strategic Defense Initiative, the nuclear test ban and other key issues appear as wide as they were when Reagan and Gorbachev met last November in Geneva.

Diplomatic contacts between Soviet and American officials in Moscow have intensified. A few days ago, U.S. Ambassador Arthur Hartman held a lengthy session with Central Committee Secretary Anatoliy Dobrynin. Bilateral talks have been held in Stockholm on the Middle East, others are opening this week in Geneva on SALT II and nuclear testing, and "a lot of others" will follow, a senior western diplomat here said.

"These are all sessions to test the waters for a summit," the diplomat said, and for a summit preparatory meeting between Secretary of State George P. Shultz and Soviet Foreign Minister Eduard Shevardnadze, likely to be held in September in New York.

Despite the dialogue, compromise is still elusive. Moscow and Washington remain far apart even on the nature of a summit agenda. "Just because we agree to talks doesn't mean that we want to talk about the same thing," a U.S. official here said. He said that in meetings Tuesday in Geneva on SALT II, U.S. officials will revive charges about Soviet violations of the treaty. And the Soviets are expected to continue a bid to rescue the accord, which Reagan has said the United States no longer plans to honor.

Although Moscow has calmed the shrill campaign against SDI that preceded the last summit, the space weapons program remains the key stumbling block to a superpower arms control accord, French President Francois Mitterrand said in a July 10 press conference here.

Without a mood of compromise, western diplomats in Moscow are skeptical about the possibilities of a successful second summit, even though they are more confident that one will take place.

Some of them have expressed fears that a standoff over a moratorium on nuclear testing, coupled with the dispute over SDI, will thwart an agreement curtailing strategic nuclear weapons and inhibit the superpower dialogue.

"In addition," one senior western diplomat said, "there is a sense that an opportunity was lost after the November summit, and neither side knows quite how to regain it."

Moscow has begun to press its campaign to get Washington to join the Soviet moratorium on nuclear weapons testing, now nearly a year old. The Foreign Ministry has dispatched envoys around Europe to discuss that issue and others. The Soviet Academy of Sciences also held a conference of test ban proponents, drawing scientists from all over the world.

But the Reagan administration remains adamantly opposed to a ban, a U.S. diplomat here said. In bilateral talks on nuclear testing to be held in Geneva this week, U.S. officials plan to discuss ways to verify a nuclear test and determine its magnitude, as a way of policing the threshold test ban treaty, the diplomat said.

The recipe for a grand U.S.-Soviet compromise on arms control still exists, some western and Soviet arms control experts here feel.

Moscow paved the way with its arms control proposals last month in Geneva, they said. On June 11, Soviet negotiators proposed a one-third reduction of nuclear warheads on both sides, and a mutual limitation on strategic weapons. In exchange, the Soviets asked Washington to restrict its SDI research to the laboratory and to agree to a 15-year extension of the 1972 Antiballistic Missile Treaty.

The proposals -- reportedly the first new elements the Soviets had introduced in Geneva since last fall, were viewed here as the first step toward finalizing agreements U.S. and Soviet officials had discussed during events surrounding the summit last November. "In one day the Soviets actually formally proposed concessions they had been hinting at for months," one U.S. official said of the June 11 proposals.

The proposals to reduce warheads were a modified version of the "deep cuts" that Reagan and Gorbachev said they favored last fall.

The offer to restrict SDI research to the laboratory was a clear acknowledgement that the Soviets were willing to tolerate space defense research under existing treaties.

"As negotiating positions, they offered more promise than anything the Soviets put forward in years," said one western arms analyst here.

By prolonging its response, Washington has "taken away some of the momentum" toward an arms compromise, a western analyst here said.

With the date and agenda for the summit still open, some of the European allies, bracing for a prolonged superpower stand-off on the major arms control issues, are more hopeful for an agreement on chemical weapons, troop reductions in Central Europe, or other conventional strategic accords.

Last week, Gorbachev, in choosing private American citizens as his conversation partners, demonstrated the difficulties that forging a dialogue with the Reagan administration poses in Moscow. He met with former president Richard M. Nixon, Natural Resources Defense Council scientist Thomas Cochran and television executive Ted Turner, all proponents of a kind of detente and arms control compromise that Soviet officials consider a counterweight to White House positions.

Even negotiations for the just-concluded international Goodwill Games indicated some of the difficulties of compromising on sticky political issues between the superpowers.

Turner broadcasting executive Robert Wussler said in an interview that he "fought hard" for Soviet officials to include Israel and South Korea among the 80-odd countries asked to join the games. But when asked why the two countries -- which do not have diplomatic relations with Moscow -- were not invited, Soviet sports official Marat Gramov said yesterday, "as far as I know, no one approached us from South Korea and Israel" about participation.