The Reagan administration yesterday rejected a Soviet proposal for a five-month moratorium on nuclear weapons testing, but issued an invitation to the Soviets to monitor a U.S. nuclear explosion at the Nevada Test Site, the White House announced.

The Soviets said they would go ahead with a unilateral moratorium on testing, and dismissed the invitation to monitor a U.S. explosion as a ploy to divert attention from their offer.

The rapid-fire proposals came on a day of superpower posturing that appeared to be aimed at influencing world opinion before the scheduled November summit in Geneva between President Reagan and Soviet leader Mikhail Gorbachev.

In a letter delivered in Moscow yesterday, Reagan invited a team of Soviet experts to measure a U.S. nuclear test. Reagan also offered to allow Soviet experts to examine data from a U.S. nuclear test last April to prove that it did not exceed the 150-kiloton limit set by treaty, officials said.

Presidential spokesman Larry Speakes said the "unconditional" and "unilateral" invitation for the Soviets to monitor a U.S. nuclear explosion "clearly demonstrates the U.S. intention to go the extra mile" in nuclear arms negotiations. Last September, Reagan had proposed an exchange of experts to monitor nuclear explosions, but the Soviets had not agreed.

The letter to Gorbachev, which Reagan signed over the weekend at Camp David, also included "concepts" for "trying to set a climate for the resolution of problems" before the Geneva summit, a senior official said. The letter "is kind of a forward-looking expression of his hope that we can make some headway," the official added.

Two hours after the Reagan invitation was disclosed, Gorbachev announced that the Soviets would impose a moratorium on nuclear testing starting Aug. 6 -- the 40th anniversary of the dropping of a nuclear bomb on Hiroshima -- through next Jan. 1. Gorbachev, in a statement published by the official Soviet news agency Tass and read on national television news, said the proposal would remain in effect longer if the United States halts nuclear testing.

But a senior administration official, who spoke to reporters on condition he not be identified, rejected the proposal. He said the Soviets have accelerated their testing in recent months, putting them in position not to need further testing this year and to "break out" with faster testing next year "without real costs to Soviet programs."

The official also pointed to a similar spurt of Soviet testing in 1961 following a moratorium that was not monitored by inspections from both sides, and recalled that President John F. Kennedy had said the United States would "never again" engage in such a moratorium.

Secretary of State George P. Shultz told reporters en route to Helsinki, Finland, yesterday that the Soviets had conducted three nuclear tests last week, just before issuing the moratorium proposal.

According to estimates by Swedish military scientists, which parallel those of the United States, the Soviets exploded eight underground nuclear devices this year, compared with nine detonated by the United States. The Soviets detonated 27 devices last year, compared with 16 by the United States. Some of the Soviet explosions were for nonmilitary projects. Atmospheric testing has been banned since 1963.

After Reagan proposed an exchange of observers in his speech Sept. 24 to the U.N. General Assembly, the Soviets rejected it. Then U.S. policymakers began work on a "unilateral offer" for the Soviets to monitor a U.S. test, administration sources said yesterday.

This proposal went through eight months of wrangling, officials said. A Pentagon official said yesterday that Reagan two weeks ago approved making the unilateral offer to Gorbachev. One administration source faulted White House and State Department officials for the delay, which made it appear designed to counter what he called a Soviet propaganda move.

A flurry of activity took place over the weekend, according to the senior official who spoke to reporters. He denied that the White House had quickly prepared its invitation in anticipation of the Soviet moratorium. But he acknowledged the White House was aware of a possible Soviet initiative on nuclear testing when Reagan signed the letter at Camp David, apparently on Saturday. The Reagan letter was not changed when the Soviets notified the administration Sunday of their plans to call for a moratorium Monday in a Soviet publication, "Agricultural Life."

As a result, the Reagan letter arriving in Moscow yesterday did not specifically respond to the moratorium proposal, and other officials said a second message to the Soviets may be forthcoming.

The administration has not pushed the Senate for ratification of two treaties limiting nuclear testing: the Peaceful Nuclear Explosion Treaty and the Threshold Test Ban Treaty. Both were signed by President Gerald R. Ford, but the Reagan administration has said verification provisions are inadequate.

In the Senate yesterday, Sen. Edward M. Kennedy (D-Mass.) introduced a resolution calling for renewed talks aimed at achieving a comprehensive test ban. A vote on the measure was set for today.

Senate Minority Whip Alan Cranston (D-Calif.) said the Soviets "made a good proposal" for a moratorium that the United States should accept, and "we made a good proposal also" that Moscow should have accepted. "But I wish both sides would get together instead of trying to make propaganda points over the other," Cranston said. "This is too serious a matter for both the Soviet Union and the United States to be playing 'Can You Top This?.' "