President Reagan said yesterday he remains "hopeful" for a superpower summit in the United States, but senior administration officials said they were taken aback by the new demand of Soviet leader Mikhail Gorbachev that the summit be linked to concessions on Reagan's missile-defense program.

The officials said they were also startled by new Soviet proposals that appeared to widen differences with the United States on the issues of strategic, or long-range, nuclear arms and on medium-range missiles.

Presidential spokesman Marlin Fitzwater said Gorbachev has made the Strategic Defense Initiative a "roadblock" to the summit in his discussions with Secretary of State George P. Shultz. He said Reagan is "wondering like the rest of us" if Gorbachev "is getting cold feet on peace."

"We have to wonder whether there is some other fear that raises this issue," Fitzwater said. "It certainly raises a lot of hard questions on his intentions."

A senior official speculated that Gorbachev has decided he does not want to come to the United States at this time, possibly because of pressures in the Soviet Union or security concerns.

The administration still maintains that the next meeting between Reagan and Gorbachev should be the long-promised U.S. summit, but they also hinted that Reagan would be willing to meet the Soviet leader on neutral territory to sign a treaty eliminating medium-range and shorter-range missiles. "This is a stumbling block, a delay," the senior official said. "But an agreement is still the most important thing; the summit is secondary."

The officials said it is possible that a treaty could be concluded without a meeting of the two leaders, but one Reagan aide said it would be unlikely that Reagan would let his first major arms-control accord be signed by Shultz and Soviet Foreign Minister Eduard Shevardnadze.

White House officials said as late as Thursday evening they expected a summit announcement to be made yesterday after the Shultz meeting, and they were surprised and puzzled when it was not. Shultz and national security adviser Frank C. Carlucci informed Reagan of the developments in a phone call from Moscow.

Reagan, in an interview yesterday with correspondents from Western European newspapers, said "I'm hopeful" the summit will take place. "It was just a case of -- they have said they want a -- such a thing and agreed to it and to be held here in this country, but so far have not set a date. So, I'll remain hopeful that we can have it, yes."

Asked whether the setback in Moscow "heralds a cooler period in U.S.-Soviet relations," Reagan said, "I have to believe that there is an effort being made on their part as well as ours to make the cold war a little warmer in the right way. Let's say, a little less cold, but also a little less war."

Reagan said he would not modify his position on the missile defense system. "I cannot make that a bargaining chip," he said. "We have the prospect of a defensive system that could practically make nuclear missiles obsolete."

Reagan had said recently that he believed the Soviets had no longer insisted on linkage between the space defense issues and the prospective missile treaty. The revival of this linkage in the Shultz-Gorbachev talks disturbed White House aides.

Gorbachev's unwillingness to set a summit date contrasted with Soviet behavior last spring, when dates were discussed.

On strategic weapons, State Department officials said they were surprised by the new Soviet proposals that appeared to widen differences between the superpowers. According to the Soviet news agency Tass, for example, Gorbachev told Shultz that both sides should begin a moratorium on "production, testing and deployment" of the medium-range and short-range missiles included in the proposed intermediate-range nuclear force treaty beginning Nov. 1.

The officials said such a moratorium would heavily favor the Soviet Union, which now has roughly 1,200 more medium-range and short-range missile warheads deployed than the United States.

They said missile production, testing and deployment should be stopped only after an INF treaty takes effect.

"The proposal is obviously designed to play well in Western Europe, where there is growing sentiment that further U.S. deployment of Pershing II and ground-launched cruise missiles should be postponed because an agreement is imminent," a State Department official said.

Compliance with such a moratorium could not be verified, the official said, and NATO acceptance would ease pressure on the Soviets to complete the agreement.

On strategic arms, where the two sides are considered even further apart, Tass said Gorbachev proposed that both sides sharply limit the number of warheads permitted on land- and sea-based intercontinental ballistic missiles. But one knowledgeable U.S. official said the proposed Soviet cap of 1,800 to 2,000 warheads on submarine-based missiles was "a notable step backward and far too low to be acceptable."

The official added that a newly proposed Soviet limit of 800 to 900 cruise missiles deployed on strategic bombers was also much lower than the Reagan administration has proposed.

The official said the Soviets previously indicated they might accept a U.S.-proposed limit of 3,600 submarine warheads. U.S. officials also hoped the Soviets would agree to mutual deployment of up to 1,500 cruise missiles on strategic bombers.

However, the official said the administration would probably welcome a third Soviet proposal to limit land-based strategic missiles to 3,300, as the U.S. negotiators have proposed in Geneva. "The difficulty is that the new Soviet limits appear to be packaged together," the official said.