Top administration officials expressed renewed concern today about Soviet delays in setting a date for the next summit meeting, scheduled to be held in the United States.

Although President Reagan's first choice was to give Soviet leader Mikhail Gorbachev a tour of the United States in June, White House officials said that is rapidly becoming impossible because the president's schedule is being filled for the month, and there would not be enough time for preparations.

"The only way we could do it in June now would be to have a Washington summit, not the tour of America," one official said. However, officials said a July summit was still feasible.

Presidential spokesman Larry Speakes said today that "time is getting close, it is getting critical" to carry out "effective planning" for a summer summit.

Secretary of State George P. Shultz, interviewed on NBC's "Today," recalled that Reagan had issued an invitation in Geneva for Gorbachev to come to the United States this year. "They should come to the United States the latter part of June, the latter part of July, as soon as it suits him and discuss not only the question of nuclear testing but the whole range of issues we have before us," Shultz said.

"And that offer is open and it's a mystery to us -- I'm sure he's anxious to meet, as he says -- why doesn't he accept that, and let's get a date set and let's get working," he added.

Georgi Arbatov, a Soviet expert on U.S. affairs, interviewed on the same program, accused the United States of backing away from the spirit of the Geneva meeting last November, but said the option of a summit this year is still "open."

Shultz also criticized Gorbachev's weekend proposal for a summit in Europe to discuss nuclear testing, which Reagan rejected, saying the two sides need to sit down privately and talk.

"To make a proposal for a major meeting between the president of the United States and the general secretary of the Soviet Union, to make it over television with no pre-warning or anything, is to simply put it into the public domain and not have it explored carefully," he said.

Speakes, discussing Shultz's call for more quiet diplomacy, said the secretary had also been critical of U.S. officials in one instance earlier this month for making public a proposal on nuclear testing verification before it could be presented privately to the Soviets.

About the summit, a senior White House official said of the Soviets, "They know we're sitting here waiting for an answer to a summit date. Why would we meet on a one-issue agenda on something we have clear views about? . . . It doesn't seem like anything that would bear fruit. Why did they do it?"

Other White House officials say that Ambassador Anatoliy Dobrynin may be bringing with him a summit date on his return to Washington soon. They have complained that the Soviets appeared to be trying to extract concessions on arms control issues in exchange for a summit date -- concessions they say Reagan will not give.

The senior official said there is a sense of "bewilderment" in the administration about Soviet intentions on the summit, but that officials hope to hold Gorbachev to the agreement made in Geneva, pointing out that it was widely publicized and would appear to be a major retreat if he did not come.