President Reagan has sent Soviet leader Mikhail Gorbachev a letter, described by one official as "conciliatory," offering to discuss on-site inspection of nuclear testing in both countries, administration sources said yesterday.

The United States publicly rejected a Dec. 5 offer by Gorbachev to open up some Soviet nuclear test sites for inspection in return for U.S. participation in a Soviet moratorium on underground nuclear testing. The United States wants to continue underground testing to develop new weapons, including possible components of the Strategic Defense Initiative, or "Star Wars," missile-defense plan.

But U.S. officials said Reagan was encouraged by the tone of the Soviet proposal and by Gorbachev's apparent willingness to consider on-site inspection.

Disclosure of the Reagan letter came on a day when the president formally submitted a written report to Congress claiming that the Soviets have gained militarily through violations of treaties governing nuclear, chemical and biological weapons. Administration spokesmen, led by Defense Secretary Caspar W. Weinberger, have frequently made such accusations in the past.

"Through its noncompliance, the Soviet Union has made military gains in the areas of strategic offensive arms as well as chemical, biological and toxin weapons," the presidential report said.

Despite a claim that these violations "darken the atmosphere" for new arms-control accords, the language of the president's report -- and of senior officials who briefed reporters on its contents -- was generally mild.

Also yesterday, White House spokesman Larry Speakes told reporters that Reagan will continue to abide by the provisions of the SALT II arms-control agreement that -- had it been ratified -- would expire Dec. 31.

"The policy is in place," Speakes said. "Our policy on SALT II is that we've indicated we will live under the agreements of SALT II and not violate them. And until we say differently, the policy remains the same, and no announcement is required on Dec. 31."

Later, deputy press secretary Edward P. Djerejian said that the Soviets had complied with treaties on nuclear proliferation, Antarctica and outer space and with "significant provisions" of both SALT treaties, but he added that "selective adherence is not enough."

Pressure is growing on the president, particularly from the Pentagon and conservatives in his party, to match his accusations of Soviet violations with deeds. Reagan will face a critical decision on SALT II limits this spring when the next Trident submarine, capable of carrying 24 muiltiwarhead missiles, is scheduled for sea trials. Those missiles will put the U.S. total above the SALT II limit and require dismantling of two Poseidon submarines to continue adherence to the treaty.

"Spring is the hard target date" for continuing SALT restraints, a White House official said yesterday.

Last week, Sen. Jesse Helms (R-N.C.) sent a letter to the president warning he would fight any administration decision to continue the "policy of interim restraint" on SALT II past the end of the year, according to Senate sources.

Helms asked that the Justice Department report to him on the legality of destroying Poseidon submarines "in order to comply with the provisions of the proposed, but unratified, SALT II treaty."

The 14-page unclassified report, which Reagan sent to Congress yesterday on purported Soviet violations, was accompanied by a longer classified report. Among other accusations, the president charged that the Soviets had violated the SALT II pact by building a new radar at Krasnoyarsk, by developing and deploying a new intercontinental ballistic missile -- the SS25 -- and by "deliberate concealment" of missile launchers during testing.

A senior official said Reagan's "conciliatory" letter to Gorbachev was "on its way" to Moscow. The letter repeats a proposal, which was rejected by Gorbachev, inviting the Soviets to attend a U.S. underground nuclear test in Nevada.

Last August, in one of his principal presummit proposals, Gorbachev announced a unilateral moratorium and called for U.S. participation. The proposal was turned down by Reagan, and the moratorium is scheduled to end Jan. 1.

The new Reagan letter did not alter U.S. opposition to the Soviet moratorium but did react approvingly to what the senior official called "the positive aspects" of Gorbachev's latest proposal.

"We're intrigued with apparent Soviet interest in on-site inspection for verification purposes," the official said. "That's something new from them that deserves to be taken seriously."

The U.S. program of underground nuclear tests is scheduled to resume Saturday, when an oft-postponed experiment to see if a hydrogen bomb explosion could be used as part of a Star Wars defense is due to take place, according to officials at the test site in Nevada.