The Soviet Union made public today an offer to open up its nuclear test sites for some kind of inspection if the United States joined in a four-month-old Soviet moratorium on nuclear testing.

The Soviet offer, revealed by the Communist Party newspaper Pravda, was seen by western diplomats here as an effort to put more public opinion pressure on the United States to join the unilateral Soviet moratorium put into effect on Aug. 6, the anniversary of the Hiroshima bombing, and to last until Jan. 1, or longer if Washington agreed to join.

Sources in Washington said that the Soviet proposal first was made in a private letter on Dec. 5 from Soviet leader Mikhail Gorbachev to President Reagan, Washington Post staff writer Walter Pincus reported.

The Soviet proposal for some, still undefined, on-site inspection addresses one of the objections that has been raised in the past by Washington to repeated calls from the Kremlin for a joint halt to testing.

But U.S. officials said in Washington that it does not deal with what has more recently emerged as the main White House objection to a test moratorium -- the need to keep testing until there are deep cuts in offensive nuclear stockpiles and as long as such weapons are required to deter attack.

U.S. officials in Washington also pointed out today that this is not the first time the Soviets have proposed some form of on-site inspection for nuclear tests. In the 1976 treaty governing peaceful nuclear explosions, which was signed by President Ford but never ratified by the U.S. government, both Moscow and Washington agreed to on-site inspections. U.S., Soviet and British negotiators also agreed on the concept of on-site inspections during negotiations on a comprehensive test ban, which were broken off in 1979.

Nevertheless, administration officials have been meeting for two days to prepare a response to the Gorbachev letter. Officials said that they recognize the public relations challenge the latest Soviet offer represents.

Washington rejected the Soviet moratorium proposal of last summer, offering instead to exchange inspection teams. The United States has held the position that without inspections, a total test ban would be difficult to verify.

Western experts have also argued that the Soviets advanced the moratorium after finishing a round of tests, while the United States is now in a phase of updating its nuclear arsenal.

Today's Pravda article said that the Soviet Union would accept an international verification system that would place special monitoring stations in third countries.

It added: "The Soviet Union is prepared to go even further. It stands for coming to terms with the United States . . . also on certain measures of on-site verification to remove the possible doubts about compliance with such a moratorium."

The Soviet move was seen here as a further sign that, one month after the Reagan-Gorbachev summit in Geneva, the Kremlin is determined to keep the initiative in the East-West dialogue, diplomats noted.

Tonight a correspondent on the main Soviet television news program, continuing a new trend of "man in the street" interviews, stopped American and British tourists in Moscow to ask them how they assessed the Soviet moratorium.

The Pravda article did not elaborate on what the Soviets meant by "certain measures of on-site verification," and some diplomats cautioned that the terms and conditions of the inspection visits would be important to clarify.

In a conversation yesterday with Drs. Bernard Lown and Yevgeny Chazov, representatives of the Nobel Peace Prize-winning International Physicians for the Prevention of Nuclear War, Gorbachev raised the possibility of on-site inspections in the case of "suspicious events."

Chazov and Lown had sought a commitment from Gorbachev to continue the moratorium past the Jan. 1 deadline. But according to Lown, Gorbachev left the impression that unless the United States agreed to halt testing, the Soviet Union would resume after New Year's Day.

Pravda reinforced that impression today, saying, "For obvious reasons, in the face of military preparations overseas, the U.S.S.R. cannot sacrifice the interests of its security and the security of its allies and friends."

Pravda today again stressed the Soviet view that a halt to nuclear testing would be a "major landmark on the way toward eliminating the nuclear danger . . . . A mutual moratorium cannot draw any objections, while the benefit from it would be big," it said.

Since Gorbachev first announced the moratorium last July, the Soviets have insisted that verification of a total ban can be handled by existing technology -- seismological monitoring from nearby countries. Besides insisting on a more exact system of verification, the United States has argued that a test ban should be negotiated, not imposed by unilateral or mutual moratorium.

Today's Pravda article urged a prompt resumption of the talks on a comprehensive test ban treaty.

Two other treaties signed by the Soviet Union and the United States -- the threshold test ban treaty of 1974 and the peaceful nuclear explosions treaty of 1976 -- have never been sent to the U.S. Senate for eventual ratification, also because of debate over verification and compliance. Both countries have said they would honor the unratified treaties, which limited underground explosions to 150 kilotons, but each has accused the other of violating the limit.

In Washington today, White House spokesman Larry Speakes divided the two issues of on-site inspection and a test moratorium. Speakes welcomed any progress on on-site inspections and saw the Soviet proposal as appearing to respond to Reagan's desire for improved verification of the two signed but unratified treaties.

But as for a moratorium, he said, "we would not agree at this time" because continued weapons testing is required "where both the U.S. and our allies must rely on nuclear weapons to deter aggression."