The Reagan administration yesterday said it was disappointed at the initial Soviet rejection of President Reagan's interim nuclear arms proposal but insisted that "there is still life" in the U.S. plan and suggested some cause for hope in the "relatively restrained" tone of the Soviet response.

In an official State Department statement and a subsequent briefing for reporters, the administration also sought to rebut the main criticism of the Reagan proposal within hours after Soviet Foreign Minister Andrei A. Gromyko told a Moscow press conference that the U.S. plan is "unacceptable."

Gromyko's rejection of Reagan's offer to discuss some equal level of intermediate-range missile warheads based in western Europe and the Soviet Union below the planned deployment of 572 new U.S. missiles and the larger existing Soviet force was not unexpected.

But it comes as large-scale demonstrations against the U.S. deployments are beginning in Britain and Europe, and it will undoubtedly heighten the tension that already surrounds the missile question.

Yesterday, senior officials warned that "it would be wrong of the Soviets" to view these protests "as demonstrating a lack of will" in the West to go ahead with deployments, scheduled to begin in December. They noted that all allied governments have voiced strong public support for the Reagan intiative.

They said they recognize European concerns on the missile issue generally, but they stressed that there was widespread agreement that Moscow must not be allowed a monopoly on weapons such as the 351 mobile, triple-warhead SS20 missiles already fielded that can strike allied targets up to about 3,000 miles away.

Aside from noting that Gromyko's "tone was relatively restrained, by Soviet standards," the statement also pointed out that Moscow had agreed to return to the currently recessed Geneva negotiations earlier than planned, at Washington's request. Officials also pointed out that the Soviets have at times accepted things that they initially rejected, such as the basic decision to negotiate on the missile issue, which Moscow seemed to have ruled out in 1979 after NATO decided to deploy new missiles.

"The Soviet Union owes the world a more positive response," the U.S. statement said. Briefing officials, who declined to be identified, claimed the Soviets "have every reason to be concerned about conveying the impression they are unwilling to agree to equality."

The U.S. and Soviet views of equality, however, are vastly different.

Gromyko claims that a balance exists and that the United States has an edge in some areas. He argues that the Reagan plan does not take into account 162 British and French nuclear-tipped missiles; that it does not cover aircraft capable of reaching the Soviet Union with atomic bombs from European and Asian bases, or aircraft carriers, and that it includes an unreasonable demand that the Soviets dismantle their missiles in Asia as well as in Europe.

In rebutting these claims, American officials point out that in 1979, when the Soviets had more than 400 warheads deployed on SS20 missiles, Soviet leader Leonid I. Brezhnev claimed then that a balance existed. Today there are more than 1,050 SS20 warheads deployed on more than 350 missiles, and the Soviets add roughly one new missile each week. The West still has no such weapons, yet the Soviets continue to claim that a balance exists, the officials said.

Washington claims that the missiles, which can hit targets in 15 minutes, should be the focus of the initial phase of negotiations and that to include aircraft now would divert attention from the more urgent problem of missiles. But even if aircraft were counted, the official NATO analysis shows 2,500 Soviet and Warsaw Pact aircraft capable of hitting western Europe with atomic bombs against 450 U.S. and allied attack planes.

Officials reiterated that the 144 submarine-based British and French missiles and the 18 French land-based missiles are sovereign forces not controlled by NATO and are meant as a last-ditch deterrent against atomic attacks on those countries. They cannot deter attacks on other allied countries, which is why American missiles must be deployed to link the overall security of Europe to the U.S. nuclear deterrent.

The officials also said that the Soviets have 950 other longer-range, strategic submarine-based missiles, a force larger than the 550 U.S. strategic missiles on submarines plus the French and British forces.

The Reagan administration also maintains that because the SS20s are mobile, any agreement must also include limits on deployments in the Asian portions of the Soviet Union. Some 108 of the 351 SS20s are in the eastern Soviet Union, presumably aimed at China, Japan and South Korea. American officials say that U.S. tactical fighter-bombers based in Japan and Korea are no comparison to the quick-striking and invulnerable SS20s in terms of a threat. The United States, therefore, also wants any agreement to prevent the shifting to Asia of missiles removed from Europe.

Although the administration has always talked of a "global" ban on the SS20, this recent emphasis on including Asia is a major new complication in the negotiations.

The Soviets also still hve 240 older SS4 and SS5 single-warhead missiles, but officials acknowledged that these are being dismantled and that Moscow probably intends to get rid of all of them as the SS20s are fielded. Five years ago, they said, there were about 600 of these missiles.

Officials acknowledged that even if the West deploys all 572 of the new single-warhead U.S. missiles, it would not achieve equality with the more than 1,000 Soviet SS20 warheads. But they said such a force was a good deterrent, and since that was the number agreed to in 1979 by NATO, the West would stick to it.

Although the U.S. statement said "we are disappointed at this unconstructive...Soviet reaction" to Reagan's interim proposal, officials expressed hope that Moscow would adopt "a more flexible view" as it studies the idea during the recess.