Former president Richard Nixon met for nearly two hours with Soviet leader Mikhail Gorbachev in the Kremlin today, climaxing a week of talks he has held with Moscow's leading American experts.

Nixon and Gorbachev concentrated their discussion, held in the Soviet leader's office, on the current state of relations between the United States and the Soviet Union, Nixon spokesman John Taylor said. Anatoliy Dobrynin, Kremlin foreign policy adviser, Soviet Central Committee secretary, and former envoy to the United States, sat in on the talks, Taylor said.

Dobrynin, whose links with Nixon date back nearly two decades, helped arrange the former president's visit here, according to Taylor.

Nixon's 1 hour and 40 minute conversation with Gorbachev was "detailed and frank," the Soviet news agency Tass reported in a brief dispatch. The discussion was also reported on the the Soviet evening news program Vremya, but neither Taylor nor the Soviet media provided details.

Western diplomats view the meeting as part of the Kremlin's recent efforts to demonstrate its willingness to open various channels of communication with the West, particularly among arms control proponents. In Moscow Nixon is viewed more as a champion of detente than as the only president in U.S. history to resign. Nixon left office in 1974 in the heat of the Watergate scandal.

Recent public statements from Moscow on President Reagan's proposed Strategic Defense Initiative have contained ideas similar to those Nixon put forth in a fall 1985 article in Foreign Affairs magazine. In the article, Nixon wrote that the most useful type of defensive system would be one that offered partial "defense of our missile fields," not the more exotic antisatellite and space-based weaponry that is envisioned by Reagan, and that now seems to alarm the Soviets the most.

The meeting with Gorbachev is also helpful to Nixon's ongoing image building campaign, diplomats said. It is consistent with his recent efforts to reassert his voice in international affairs, highlighted by trips to Cairo, Peking, Paris and Jeddah.

The Nixon-Gorbachev meeting came amid a rush of public and private initiatives here attempting to influence U.S.-Soviet relations.

Shortly before receiving Nixon, Gorbachev met with American television executive Ted Turner, head of Turner Broadcasting Systems and initiator of the international Goodwill Games now drawing to a close in the Soviet capital. Gorbachev praised the 17 days of contests involving hundreds of Soviet, U.S., and other foreign athletes as "a real positive force in U.S.-Soviet relations," according to Turner Broadcasting Systems spokesman Ken Bastian, following the hour-long meeting in the Kremlin.

Nixon arrived in Moscow last Saturday as U.S. and Soviet officials here quietly continued the diplomatic legwork to establish the terms for a second summit between Reagan and Gorbachev, which was due to take place this year, and a summit preparatory meeting between Secretary of State George P. Schultz and Soviet Foreign Minister Eduard Shevardnadze.

The Shultz-Shevardnadze meeting "looks like" it will take place in New York in September, a senior western envoy said here today. But it, and the summit, which Reagan and Gorbachev agreed last November to hold this year, remain unscheduled.

Western diplomats in Moscow linked Nixon's visit to the diplomatic activity on the summit, although Nixon spokesman Taylor has stressed that the trip is a "private, fact-finding mission," and that the former president is not acting as a liaison between the Reagan administration and the Kremlin.

Nixon discussed his current Moscow trip in a telephone call with Reagan last Friday, just before his departure for Moscow, and plans to report to Reagan after returning to the United States, Taylor said.