Departing Soviet Ambassador Anatoliy Dobrynin and Secretary of State George P. Shultz took the first step yesterday toward agreement on the next U.S.-Soviet summit meeting by discussing plans for a high-level preparatory meeting to be held in Washington, according to administration officials.

The preparatory session would be conducted here by Soviet Foreign Minister Eduard Shevardnadze with President Reagan, Shultz and other senior officials at a time yet to be determined. A U.S. source said part of yesterday's 90-minute breakfast meeting at the State Department, which was also attended by presidential national security affairs adviser John M. Poindexter, was devoted to exploring possible dates for the Shevardnadze visit.

Dobrynin may cast further light on the timing and substantive prospects of the next summit meeting during a farewell call on President Reagan at the White House this morning. The veteran Soviet diplomat is winding up 24 years as ambassador here to become chief of the international department of the Soviet Communist Party Central Committee, a senior position in the Communist Party leadership.

White House chief of staff Donald T. Regan, at a luncheon with reporters several hours after the Shultz-Dobrynin meeting, said a June or July summit meeting in the United States as originally proposed by Reagan is "still possible" although advance teams "would have to do a lot of work."

However, a knowledgeable Soviet source said that "after November" would be the right time for the next meeting of Reagan with Soviet leader Mikhail Gorbachev. June is "too early" because preparatory work has not been started, he said. The delay was attributed to to Soviet displeasure with events and statements from Washington since the Nov. 19-21 Geneva meeting of Reagan and Gorbachev.

An underground U.S. nuclear weapons test at the Nevada Test Site is also scheduled to take place this morning, shortly after Dobrynin's meeting with Reagan. Administration officials said the timing of the blast, which may cause the Soviet Union to resume its own nuclear tests after an eight-month hiatus, was not planned to coincide with the Dobrynin visit.

"It is purely coincidental," said a senior U.S. official of the nuclear test, who said it had been scheduled well in advance of Dobrynin's call on Reagan. The official said there had been discussion within the administration of postponing the nuclear test for a few days in view of Dobrynin's visit but that, especially after Gorbachev's March 29 speech on nuclear testing, which was regarded in the administration as a propaganda effort, it was decided to permit the explosion to go ahead as planned.

Rep. Dante B. Fascell (D-Fla.), Foreign Affairs Committee chairman, who met Gorbachev in Moscow last Friday, said that detonating a nuclear explosion today "certainly is not going to help matters any" in relations with the Soviets. "Unless it is absolutely necessary to do it right at this time I don't see why it is being done," Fascell said after a White House meeting with Reagan.

"It appears to me that the window of opportunity to get a real agreement with respect to arms control and reducing tension is a very narrow window and we'd better grab it right now," Fascell said.

Rep. William S. Broomfield (Mich.), ranking Republican on the Foreign Affairs Committee, who also met Gorbachev last Friday, said his assessment is that "relations are strained" at present between the two nuclear superpowers. Broomfield said Gorbachev seemed particularly "livid" about the recent U.S. demand that the Soviet mission to the United Nations be reduced by more than 100 officers as a counterintelligence measure.

Soviet sources said Dobrynin's new post as chief of the Central Committee's international department will deal with the full range of Soviet foreign policy issues, including East-West diplomacy. Under its previous chief, 81-year-old Boris Ponomarev, the department emphasized relations with sister communist parties. The change, according to the sources, will make Dobrynin a member of the senior Soviet leadership with a broad mandate in foreign affairs.Staff writer Ann Devroy contributed to this report.