Richard M. Nixon came back today to Moscow, where his visits as president made him an architect of detente.

It is not yet known whether Nixon will meet with Soviet leader Mikhail Gorbachev during his six-day unofficial visit. Some diplomats here found it suggestive that Nixon should appear during diplomatic maneuverings over a U.S.-Soviet summit.

Nixon, 73, had a 15-minute phone conversation with President Reagan on Friday, a spokesman said here. The State Department has insisted that the former president is not carrying any messages from the White House.

Nixon's last visit to the Soviet Union was in July 1974. In a speech then to the Soviet people, he promised to meet again with their then leader, Leonid Brezhnev. That promise was never fulfilled. A month later, Nixon became the first president in U.S. history to resign from office.

This time, he arrived as a private citizen, getting off a British Airways flight instead of Air Force One. But the Soviet government, which is sponsoring his visit, has not forgotten his former status. Nixon was picked up by a black limousine and whisked under escort to a Foreign Ministry guest house in Lenin Hills.

Nixon declined to speak to reporters and an aide said the trip was a "private, fact-finding tour, worked out mutually by him and the Soviet government."

"Now was a good time, considering his own schedule and circumstances," said John Taylor, an assistant traveling with Nixon. The former president was not accompanied by any family members.

A U.S. Embassy spokesman also insisted that the visit was "very, very private."

Nixon is scheduled to meet with Anatoliy Dobrynin, the former ambassador to Washington who is now a secretary of the Communist Party's Central Committee. The two met often during their time in Washington.

Taylor said today Nixon had requested no other meetings but noted that the former president's schedule was in the hands of his Soviet hosts. It was not known whether Nixon would travel outside of Moscow.

Nixon's associations with the Soviet Union go back to the so-called "kitchen debate" in 1959, when he and Soviet leader Nikita Khrushchev argued heatedly amidst home appliances at an American exhibition in Moscow.

Nixon, then vice president, was known for his staunch anticommunism. His conservative stance later gave him the political capital as president to help open the period of detente with the Soviet union in the early 1972, a period frequently hailed in the official press here as the shining moment in U.S.-Soviet relations.

In 1972, Nixon was the first, and only, U.S. president to pay an official visit to Moscow. During that visit, he signed the first Strategic Arms Limitation Treaty and the Anti-Ballistic Missile Treaty.

Soviet officials often speculate privately that it was Nixon's espousal of detente that brought about his downfall, not the Watergate scandal. Now the ABM treaty is again an issue in East-West relations, a key point in the debate over the development of Reagan's Strategic Defense Initiative.

A summit between Gorbachev and Reagan has been expected this year, according to the schedule adopted at the first summit in Geneva last November. But Gorbachev has insisted that the next summit should produce an accord on arms control, and not just be publicity event. He repeated this view this week in meetings with French President Francois Mitterrand.

In Washington, Post reporters added:

Knowledgeable sources said Nixon's visit was arranged hurriedly in the last week, and he had hoped to keep it secret.

The White House did not learn of Nixon's voyage to Moscow until Thursday, and Nixon's only contact with Reagan about the trip was his phone call to Reagan Friday, these sources said. Nixon carried no message from the Reagan administration to the Soviets, but the Soviets may hope to use him as a messenger back to Reagan, they added.

Nixon recently signed a contract to write a book on global politics between the present day and the year 2000, according to a source close to the former president, and he plans to focus it on Soviet-American relations. He has already talked with a number of past and present officials, including Secretary of State George P. Shultz, about his book project, this source reported.