In offering a new nuclear-arms reduction proposal to the Soviet Union last week, President Reagan acted against the advice of usually influential Defense Secretary Caspar W. Weinberger, according to administration officials.

"The president was very clear; he said it was a chance to take them up on some of their specifics," said a senior administration official familiar with the views of Reagan and Weinberger.

Another source said Weinberger was "the holdout" among a group of advisers, led by national security affairs adviser Robert C. McFarlane and specialists in the Arms Control and Disarmament Agency. They favored a specific U.S. counterproposal to a Soviet offer last month calling for a 50 percent reduction in strategic nuclear arms and severe limits on Reagan's missile defense plan, often called "Star Wars."

The sources said that Weinberger opposed the major reductions that the new U.S. proposal would require in U.S. sea-based missiles and bombers. He also raised concerns about the difficulty of verifying Soviet compliance.

Weinberger reportedly favored a rhetorical response by Reagan rather than a detailed counterproposal that would be presented to the strategic arms negotiators in Geneva. But other policy and political advisers disagreed, pointing to the public-relations advantage the Soviets had gained by offering significant reductions.

A senior official said the president had been "convinced" at an early stage that there should be a detailed U.S. response to the Soviet proposal at the negotiating table in Geneva if the analysis could be completed in time.

"He always felt it was the proper way to do it," the official said.

A Defense Department official confirmed this account and said Weinberger "recognized that the president wanted to respond." The official said Weinberger had opposed the U.S. counterproposal in writing, considered it "premature" but accepted the decision and would make no effort to undercut it.

Some officials consider Reagan's rejection of Weinberger's counsel unusual and significant. Weinberger has been an important policy adviser since his days as a key aide to Reagan when he was governor of California. He has often carried the day on national-security issues against the recommendations of Secretary of State George P. Shultz, McFarlane and the White House staff.

During Reagan's first term, Weinberger and Assistant Secretary of Defense Richard N. Perle, the Pentagon arms-control specialist, usually prevailed in bitter disputes that divided the administration in its arms-control approaches to the Soviets. Sources said that early in the second term, McFarlane, Shultz and senior adviser Paul H. Nitze made a concerted effort to "wall off" Weinberger and Perle and to obtain a presidential commitment to a new arms-control initiative.

This effort has continued, sources said, and Weinberger is not among the U.S. officials scheduled to attend the Nov. 19-20 summit meeting in Geneva between Reagan and Soviet leader Mikhail Gorbachev. Weinberger has made no secret of his desire to attend, officials said.

Despite Weinberger's failure to head off the new U.S. proposal, officials said Perle contributed several provisions that reflected the Pentagon view. One of his contributions to the plan, a proposal to ban mobile strategic missiles on both sides, drew sharp criticism Friday from key members of Congress who had helped Reagan win approval of the MX missile in return for his commitment to pursue development of the Midgetman mobile missile.

However, administration sources said the president and McFarlane agreed with Perle about the desirability of banning mobile missiles, on grounds that they are "destabilizing" to the strategic arms balance because it is difficult to verify mobile missile deployment. Proponents of a mobile missile take the opposite view, arguing that the existence of mobile weapons that the other side cannot target with confidence would eliminate the temptation to launch a first strike, since it could never fully disable the possessor of hidden mobile missiles.

The only U.S. mobile missile, the Midgetman, is on the drawing boards and not scheduled for deployment for several years. According to Weinberger, the Soviets are beginning to deploy a mobile missile, the SS25, and have developed a mobile version of a new SS24 comparable in destructive power to the immobile U.S. MX missile.

Perle also proposed that the new U.S. offer include a 50 percent cut in "throw weight," the size of the payload each side's missiles can deliver. Because Soviet missiles tend to be considerably larger than American ones, such a limit might be harder for the Soviets to meet.

The new U.S. proposal would also ban new "heavy" missiles, such as the gigantic Soviet SS18. The United States has no missiles in this category.

The new U.S. proposal contains several features that administration officials think that the Soviets will find attractive. It is "a good deal for them," a senior official said, because "it's very important for the Soviets to have specific caps on certain U.S. missiles -- that's the here and now."

The U.S. proposal adopts the Soviet concept of a 50 percent cut in strategic missiles, but redefines it so that medium-range missiles and bombers in Europe are excluded from the strategic missile count. Thus, U.S. officials count 9,000 Soviet ballistic missile warheads compared with 8,000 U.S. warheads. The new plan calls for a common ceiling of 4,500 warheads.

The United States now has deployed 2,118 warheads on land-based missiles and 5,536 warheads on submarine-based missiles. To reach the 4,500 ceiling, the United States would have to make significant reductions in its sea-based missile force, and cut the deployment of upcoming Trident II missiles. The Soviets want to limit these accurate weapons because they are the first U.S. sea-based missiles that hold the promise of being able to destroy land-based Soviet ICBMs in hardened silos.

Officials said the new U.S. proposal was drafted in 13 meetings of the Senior Arms Control Group (SAC-G), which began meeting in September, before Soviet Foreign Minister Eduard Shevardnadze had told Reagan of the new Soviet arms-reduction proposal.

After the throw-weight cut and the ban on mobile missiles was included, Perle acquiesced in the proposal, a source said, "but then he went back and used his secret weapon" in an effort to block the plan. The "secret weapon" was Weinberger, who reportedly told Reagan about two weeks ago that he opposed a specific counterproposal.

Most limited objections were raised by the Joint Chiefs of Staff, officials said. The 50 percent cut concept called for reducing the U.S. long-range bomber force to 280, slightly less than half the present 570 bombers, which includes many mothballed B52s. The chiefs said this cut would be too deep. The total in the U.S. plan was raised to 350 to obtain their support.

The chiefs also accepted another provision that caused them some concern, a ceiling of 1,500 on U.S. air-launched cruise missiles.

The U.S. proposal was finally agreed to Tuesday, while Weinberger and Perle were in Brussels attending a NATO Nuclear Planning Group meeting. They were represented at the decision-making meeting by Undersecretary Fred C. Ikle and Deputy Secretary William Howard Taft IV, who once more voiced Pentagon objections.

Reagan signed the decision document Wednesday but the U.S. side was unable to present it in Geneva because no session was scheduled that day. As a result, the president sent a message with the proposal asking the negotiators to stay in session another week.

Reagan's decision to go ahead with the counterproposal despite Pentagon objections was described by one official as "an evolution" in his dealings with the Soviets and a recognition that the Soviet proposal, despite serious flaws, had merit.

What is unknown is whether there will be a similar evolution in the way Reagan thinks about the Star Wars missile-defense plan, which he has consistently presented as a "shield" that would protect civilians from nuclear destruction. Many advocates of strategic defense, including McFarlane and former president Richard M. Nixon, say they believe that its greatest potential value is as protection for U.S. missiles in their silos rather than protecting the country.

The U.S. counterproposal does not resolve this question. It deals with strategic defense only in calling for "an exchange of information" on U.S. and Soviet defense programs and with an "open laboratories" proposal -- an offer of exchange visits to the missile-defense laboratories of both countries.

Basically, the U.S. counterproposal ignores Star Wars and offers to trade offensive weapons for other offensive weapons, leaving to the summit the question of whether Reagan would be willing to make missile defense a limited research program in return for Soviet agreement to make significant cuts in offensive nuclear weapons.