Despite an impassioned private appeal from Defense Secretary Caspar W. Weinberger, President Reagan last week rejected the Pentagon position in a series of last-minute decisions on U.S.-Soviet arms control negotiations, an action signaling his desire to move swiftly to an agreement with the Soviets and a possible summit meeting this year, senior U.S. officials said yesterday.

Reagan made his decisions Thursday in preparation for a visit here this week by Soviet Foreign Minister Eduard Shevardnadze aimed at resolving the few remaining disputes concerning a treaty to eliminate short- and medium-range missiles in Europe, the officials said. {Shevardnadze arrives in Washington today for meetings that could be critical to the Reagan presidency. Details, Page A27.}

At the same time, the president accepted Weinberger's suggestion that he maintain the current U.S. positions on the topics of strategic arms and space weapons, suggesting that the existing stalemate in these negotiations will continue unless the Soviets bring new proposals to Washington, the officials said.

Several defense officials said they were particularly unhappy about Reagan's rejection of Weinberger's plea that the new Soviet-American agreement exclude medium-range missiles with nonnuclear or "conventional" warheads. The officials said the aim of the Weinberger plea in a meeting at the Oval Office on Wednesday was to keep the prospective arms treaty from interfering with a quiet effort by the Air Force to develop such weapons for deployment in Western Europe by the late 1990s.

The United States has said that the agreement should cover nuclear-armed cruise missiles, although it has not explicitly raised the issue of excluding nonnuclear missiles with the Soviets. The Soviets have sought elimination of all missiles within the range of 330 to 3,600 miles to be covered by the agreement.

Reagan also decided to reject a Pentagon request that some of the existing U.S. medium-range missiles deployed in Western Europe or stored in the United States be retained for use by the Strategic Defense Initiative (SDI) research program aimed at developing a comprehensive ballistic missile defense, the officials said.

At present, both sides have agreed that all such missiles be eliminated, but the Defense Department wanted "to eliminate some of the missiles by flying them," one official explained. One possible use was as targets for a prospective tactical missile defense weapon; another was to launch SDI sensors and experimental weapons into space.

Reagan's decisions on both these points will be incorporated into a new version of the draft treaty that American negotiators will introduce in Geneva on Monday, officials said.

Reagan also rejected the recommendation of some Pentagon officials by deciding to show new flexibility on the issue of how rapidly U.S. medium-range missiles in Western Europe will be eliminated after a treaty is ratified. Previously, the administration maintained that no U.S. missiles would be eliminated until the Soviet Union reduced its missile force enough to equal current U.S. levels. This meant the Soviets would eliminate 1,087 warheads at the outset of the agreement, while the United States eliminated none.

But under a new proposal, which Secretary of State George P. Shultz will make during discussions with Shevardnadze on Tuesday or Wednesday, the United States will agree to reduce a small number of missiles at the outset of the agreement to demonstrate good faith.

Administration officials who support the president's recent decisions said they would remove potential stumbling blocks that would have delayed an agreement and complicated U.S. efforts to verify Soviet treaty compliance.

They said that Weinberger's proposal to exclude nonnuclear missiles was opposed by the intelligence community and the State Department because of the enormous difficulty of ensuring that missiles with ostensibly nonnuclear warheads were not in fact armed with nuclear weapons.

One official said that Weinberger, who generally backs tough proposals on verification, had surprised U.S. negotiators and other arms control officials by "demanding something that is essentially unverifiable" on the matter of nonnuclear cruise missiles.

But senior Pentagon research officials said they were concerned that a global ban on medium- and short-range missiles would seriously constrain efforts to develop a "boost-glide vehicle" that would be launched from the ground by a rocket and skim over Eastern Europe or the Soviet Union at speeds of up to 12,000 miles an hour, dropping weapons or taking pictures along the way.

One official said the Defense Department's "boost-guide vehicle" program, virtually dormant for the last few years, was suddenly "rejuvenated" by the Air Force early this summer. He added that it could be continued in the wake of the president's decision, but only if the weapon were designed to be launched from ships or airplanes, leaving it outside the scope of the agreement.

"That's going to cost us a tremendous amount of money," the official said.

Senior U.S. officials said the new decisions would still leave the two superpowers at apparent odds over the disposition of existing warheads atop medium- and short-range missiles. In recent public statements, the Soviets have sought assurances that all such warheads would be "destroyed," while the United States favors instead eliminating the warheads by dismantling them and refashioning the parts into new weapons not covered by the agreement.