MOSCOW, OCT. 16 -- U.S. Defense Secretary Richard B. Cheney began his first visit to the Soviet Union today amid signs that the Kremlin is stepping up its search for a diplomatic solution to the crisis in the Persian Gulf.

As Cheney flew into Moscow for a four-day visit, a senior Kremlin envoy who recently met with Iraqi leader Saddam Hussein left for further consultations with Western leaders on the gulf crisis. Soviet spokesmen said that the trip by Yevgeny Primakov formed part of "very serious, thought-out steps by our leadership that are aimed at avoiding war."

The crisis is likely to be a major subject in talks Wednesday between Cheney and Soviet President Mikhail Gorbachev. Although the visit was arranged well before Iraq's Aug. 2 invasion of Kuwait, it has taken on additional importance because of the crisis and the buildup of U.S. forces in Saudi Arabia.

Soviet officials said that Primakov, a member of Gorbachev's Presidential Council, would travel to Paris and Washington following meetings today with Italian officials. Primakov told a Rome news conference that he considered an Iraqi withdrawal from Kuwait both "possible and necessary" and that Moscow remains "optimistic despite everything."

Until now, the Soviet Union has insisted that it will not act as an intermediary in the gulf crisis. But Western and Arab diplomats here believe that Gorbachev, who was awarded the 1990 Nobel Peace Prize on Monday, would be willing to play the role of mediator if assured of a good chance of success.

The Soviet Union has joined the United States and other Western countries in condemning the Iraqi invasion and demanding a complete withdrawal by its former ally. But Gorbachev has also made clear that he is opposed to the use of American force to push the Iraqis out of Kuwait, a move that could seriously weaken the Kremlin's strategic interests in the region.

So far, Soviet officials have given little indication of how they view a potential settlement in the Persian Gulf. Both Iraqi and Soviet spokesmen have denied a report by the Soviet news agency Novosti that Saddam offered to withdraw his troops from most of Kuwait during his recent talks with Primakov, keeping only a few strategic islands in the north of the country.

Some Soviet commentators have expressed the belief that the Kremlin is pursuing a double-track policy, using Primakov to explore the possibility of a diplomatic solution while coordinating military action with Cheney. Soviet Foreign Minister Eduard Shevardnadze has raised the possibility of a symbolic Soviet contribution to a multilateral U.N. force if the diplomatic option fails.

Briefing reporters on the plane from London, Cheney said he wanted to find out the thinking of Soviet leaders on long-term defense plans. He said he was convinced that there had been "a fundamental shift in Soviet policy," but was not convinced that Gorbachev's proposed economic reforms would succeed.

"It is an interesting time to be arriving in Moscow -- right smack in the middle of some important debates that will shape the future of the Soviet Union," said Cheney, the second U.S. defense secretary to visit Moscow. In 1988, Frank Carlucci became the first.

Cheney refused to say whether he would press the Soviets for an assessment of Iraq's military capabilities based on their long experience of training the Iraqi army when Moscow was Baghdad's superpower patron. Last week Iraq warned the Soviet Union not to share any sensitive information with Cheney, threatening to retaliate against the more than 4,000 Soviet citizens in Iraq.

Presidential spokesman Vitaly Ignatienko said today that there would be no exchange of secret information. Last month, the Soviet chief of staff, Gen. Mikhail Moiseyev said in an interview that he had given the U.S. Embassy routine information about Soviet arms supplies to Iraq.