Prospects for an early-summer summit meeting between President Reagan and Soviet leader Mikhail Gorbachev are fading rapidly, officials from both governments say, a blow to administration hopes.

The latest snag comes over the timing of Gorbachev's response to Reagan's recent proposal to reduce intermediate-range missiles.

A Soviet diplomat said Gorbachev is not expected to reply to Reagan's offer until well after the 27th Communist Party Congress ends next week. If Gorbachev's message does not quickly lead to an agreement on when to hold the next summit, it is unlikely the two leaders could meet here in June, as the Reagan administration first proposed.

A U.S. official said the two governments need at least two months to make arrangements for a summit conference.

Both sides, however, voiced confidence that the next summit, which would mark the first visit to the United States by a Soviet leader in 13 years, would occur before this fall. The most recent U.S. proposal was for July; the Soviets informally suggested September, but were told it was too close to the November elections.

The next proposal for the timing of the summit is expected to come from the Soviets.

Hanging over the summit are new doubts about progress toward an arms agreement to eliminate or reduce U.S. and Soviet intermediate-range nuclear missiles in Europe and Asia. Gorbachev has said making progress toward ending underground nuclear tests and eliminating U.S. Pershing II and ground-launched cruise missiles and Soviet SS20s from Europe are his goals for the next summit.

The Reagan administration has opposed any halt in nuclear tests, maintaining in the president's recent letter to the Soviet leader that continued testing would be needed as long as nuclear weapons provide deterrence to war.

On the other hand, U.S. officials, who were once hopeful that an early agreement could be reached on intermediate-range missiles, are talking more cautiously about that possibility in the wake of the surprisingly cool reception such proposals received from U.S. allies.

"The allies were a driving force for the Reagan administration on arms control," one source said. "Without them," he added, "there is little pressure for the United States to take the initiative."

Another U.S. official added that the allies "are not eager for us to make any serious compromises away from the present position."

As for the summit, U.S. officials said last week there were many areas to be explored that would yield what one called "constructive engagement" for the two leaders. "It's a question of prestige for both leaders to go back to their countries with something," one official said. He added that Gorbachev could "get himself into a box" if he kept focusing on matters on which Reagan would not yield.

The official said that on the question of testing, there might be "tangible progress" toward ratification of two signed partial, nuclear testing treaties if there were progress on monitoring. Another U.S. official suggested that if the Soviets decide to end their nuclear test moratorium in April, they could invite American scientists to monitor the first underground blast.

"They would be smart to do that," one Reagan administration source said, since the U.S. position has been that it needs to monitor a Soviet test in order to calibrate monitoring devices as a step toward ratification of the treaties.

U.S. officials also see prospects for additional bilateral agreements and even "human rights progress" emerging from the summit. In addition, the two countries might approve an agreement on the proliferation of chemical weapons and could approve a draft measure on European military confidence-building measures coming out of negotiations.