Surprised Reagan administration officials expressed serious interest yesterday in the unusually comprehensive arms control proposals announced by Soviet leader Mikhail Gorbachev on the eve of today's resumption of the nuclear and space arms negotiations in Geneva.

President Reagan, in a White House statement setting the tone for the U.S. response, welcomed Gorbachev's statement as appearing "at first glance . . . constructive" in some respects. The White House statement also cautioned that many elements "are unchanged from previous Soviet positions and continue to cause us serious concern."

Of particular concern to administration officials was Gorbachev's repeated insistence on banning development, testing and deployment of "space strike arms," a Soviet term that would cover many aspects of Reagan's Strategic Defense Initiative, as a condition of the other reductions. This appeared to be intended, they said, to put more international pressure on Reagan to limit his SDI, or "Star Wars," program. Unlike many previous Soviet statements on the subject, however, Gorbachev's new proposals did not mention a ban on research on space-based weapons.

The fact that Gorbachev made his proposals on the eve of a new negotiating round in Geneva was especially intriguing to administration officials. Earlier this week Reagan was reportedly informed by his aides that very little new could be expected from the Soviets in the next round of talks, largely because Soviet leaders were thought to be preoccupied with next month's congress of the Communist Party.

A White House official said the administration is "very interested" in some of Gorbachev's extensive proposals, which touch on just about every area of arms negotiations in which the two nuclear superpowers are engaged and some new ones. The Soviet proposals cover nuclear testing, chemical weapons, conventional forces in Europe, confidence-building measures in Europe and even futuristic non-nuclear weapons such as laser beams. The Gorbachev ideas were conveyed to the White House in a letter delivered hours before they were described publicly in Moscow.

U.S. officials were particularly intrigued by Gorbachev's proposal for "complete liquidation" of U.S. and Soviet medium-range missiles in Europe. His statement was devoid of the usual Soviet demand that British and French nuclear systems be counted against weapons allowed to the United States in Europe.

Instead, Gorbachev called for Britain and France to pledge "not to build up" their small but growing nuclear arsenals.

The previous Soviet position on the British and French weapons precluded any agreement in the 1981-83 negotiations on intermediate-range nuclear forces (INF) in Europe and the earlier rounds of the current Geneva talks, in the view of the western powers.

Even before yesterday's proposals from Moscow, U.S. officials were saying that the INF area presented the greatest potential for agreement by the time of the next Reagan-Gorbachev summit this summer or fall because of earlier hints of possible Soviet flexibility. Reagan and Gorbachev endorsed the idea of an "interim INF agreement" in the final communique of their Nov. 19-21 summit.

In the area of strategic arms, the newest innovation in the Gorbachev proposal appeared to be establishment of a proposed timetable of five to eight years for the 50 percent reductions that both sides say they are seeking and eventual elimination of all nuclear weapons, even tactical nuclear weapons, by the end of the century.

Gorbachev's call for other nuclear powers to join in the reductions by 1990 appeared to be another new element.

Two earlier conditions repeated in his announcement were of concern in Washington. These were his definition of the strategic weapons to be initially reduced as those that can reach the territory of the other power. In the last round of arms talks, the United States rejected proposals based on this formulation as one-sided, since they would affect U.S. weapons based in Europe without touching any comparable category of Soviet arms.

Gorbachev also repeated the Soviet proposal for a reduction to 6,000 "nuclear charges" on each side. The United States also rejected this idea as defined by the Soviets in the last round of talks.

In extending the Soviet moratorium on underground nuclear testing by three months, Gorbachev seemed in his statement to be linking it for the first time to proposals for reductions in offensive arms. The language, however, left uncertainty on this point.

Other points of the Gorbachev statement arousing interest here included:

*His unusually positive references to verification issues, including a reference to possible on-site inspection of the dismantling of nuclear weapons sought under his proposal.

*A Soviet version of Reagan's "open laboratory" proposal regarding space research. This was presented at Geneva last Nov. 1 and discussed by Reagan at length with Gorbachev at the summit.

*An offer to declare the locations of plants for chemical-weapons production as part of an agreement to ban them. In this area, too, Gorbachev spoke of "strict control, including international on-site verifications."

*As an interim step in the field, a proposed international agreement barring transfer of chemical weapons or their deployment abroad.