President Reagan said yesterday "we're very grateful" for the latest arms-control proposals from Soviet leader Mikhail Gorbachev. But administration officials, while acknowledging that Gorbachev appeared to offer concessions, cautioned that he also repeated long-held Soviet positions that would -- unless altered -- block agreement.

Officials said the broad scope of the Gorbachev statement offered further evidence that he intends to play a far more active role in negotiating with the United States over nuclear weapons than did his immediate predecessors and that the administration will be forced to reply more imaginatively to match Gorbachev's apparent flexibility.

"For years, its been like Washington playing tennis against a backboard. We'd hit the ball and [then Soviet foreign minister Andrei] Gromyko, the backboard, would hit it back the same way," said a senior administration official. "Now there's a player on the other side of the net and you don't know where the ball is going to come back."

The sudden presentation of the Gorbachev proposal took the White House by surprise Wednesday afternoon, and officials were puzzled at how the United States had so seriously misread Soviet plans. Just as the Soviets were delivering a letter to Reagan outlining the proposal, a senior arms-control official was telling reporters at the White House that the administration did not expect the Soviets to shift positions until after the Soviet party congress at the end of next month.

Moreover, officials said they were taken aback by the comprehensive nature of the Soviet initiative, which offered new positions in almost every negotiating area. This was viewed by U.S. officials as a Soviet effort to improve the chances that the next Reagan-Gorbachev summit produces agreement in at least one area.

In a statement on the Gorbachev proposal, presidential spokesman Larry Speakes cautioned that the Soviets continued to link reductions in offensive weapons to a ban on Reagan's proposed missile defense, known as the Strategic Defense Initiative. But he described as "constructive" the Soviet proposals for new ways to verify compliance with future arms agreements.

Yesterday, officials said the White House special arms-control group (SAC-G) began studying the Gorbachev initiative, which was tabled at the opening of a new round of the nuclear and space talks in Geneva.

"The language is eerie; it's so extremely flexible that it may look better than it really is," one official said. He and other officials said the administration has to wait until the proposals are presented in detail in arms-negotiation forums before their importance can be measured.

Asked at a White House photo session whether he was encouraged by the Gorbachev statement, Reagan said, "Yes, it is different than the things we have heard in the past from Soviet leaders. It is just about the first time that anyone has ever proposed actually eliminating nuclear weapons."

Defense Secretary Caspar W. Weinberger said that while there are elements that give concern and a great deal of the Gorbachev initiative is "restatement" of past positions, there are "some things that look positive . . . that might advance the process."

Officials privately offered these assesments of specific aspects of the Gorbachev proposals:

The Soviet leader may be signaling a desire to reach agreement on one of the less-publicized forums for superpower negotiations, the Stockholm conference on confidence and security-building measures and disarmament in Europe. Gorbachev proposed dropping a requirement Moscow had demanded for advance notice of naval exercises that had been one of the major obstacles to agreement.

*On intermediate-range missiles in Europe, which officials say offer the best opportunity for the first nuclear weapons agreement in the Reagan years, Gorbachev outlined a proposal to "liquidate" missiles in Europe that at first glance resembled Reagan's own "zero option" of his first term. But officials also raised questions about what the Soviets plan to do with their medium-range missiles in the Far East and whether the entire package is linked to a compromise in Reagan's proposed missile-defense system.

One official pointed out that Gorbachev did not mention elimination of China's missiles and failed to mention Soviet medium-range missiles in the Far East, most of which are aimed at China.

*Despite the emphasis that Gorbachev put on a halt to underground nuclear testing and a resumption of talks for a comprehensive test ban, officials said yesterday the Reagan administration would not move from its position that testing had to continue as long as nuclear weapons are needed for deterrence. U.S. peace groups, which urged Gorbachev to make his offer of a three-month moratorium extension, are expected to pressure the administration to change its position. But Weinberger said the Soviets almost never test at this time of year and have begun preparations to resume testing later in the year.

*On strategic weapons, Gorbachev offered what U.S. officials described as a "road map" for reductions down to the 50 percent goal within seven years that will force Reagan administration policy-makers for the first time to determine how the U.S. force would be configured during such a reduction.