Soviet Ambassador Anatoliy Dobrynin's farewell talks in Washington have eased U.S.-Soviet relations after months of increasing tension and produced specific agreement on a series of high-level meetings between now and July, State Department officials said yesterday.

In addition to the meetings of Secretary of State George P. Shultz and Foreign Minister Eduard Shevardnadze, which were announced Tuesday and are set for May 14-16 here, the two governments have agreed to send delegations to Geneva early next month to discuss setting up "risk reduction centers" to reduce the danger of accidental war. There also will be new talks on superpower policies in Afghanistan, the Middle East, Central America and Asia before the end of June.

No date was set for the next summit meeting of President Reagan and Soviet leader Mikhail Gorbachev, which is to take place in Washington this year. State Department sources said Dobrynin did not rule out the possibility of a meeting in July, which is Reagan's preferred time, though officials on both sides said it would take unusually swift and effective work to produce a summit by then.

Dobrynin's round of meetings, including a 75-minute White House session Tuesday with Reagan, centered on preparations for the summit. Officials described the meetings with Dobrynin as wide-ranging, substantive and surprisingly positive in view of the discord and cross-purposes of recent months, including the U.S. detonation of an underground nuclear test in Nevada Thursday.

Dobrynin's rising influence in his new Moscow post as international affairs chief for the Communist Party Central Committee was dramatized by the appearance at his side here this week of Alexander Bessmertnykh, his former deputy in the Soviet Embassy and considered among the most knowledgable Soviet experts on the United States, in a new role. Bessmertnykh has been tapped to be a deputy foreign minister with special responsibility for American affairs, which is a major promotion.

The future roles of two senior figures on U.S. affairs under Andrei Gromyko, First Deputy Foreign Minister Georgi Kornienko and Deputy Foreign Minister Viktor Komplektov, are uncertain, officials said. Also unknown is the identity of Dobrynin's successor in Washington; Soviet officials said he has not been selected.

Winding up 24 years as ambassador to the United States, Dobrynin left Andrews Air Force Base late yesterday aboard a special Aeroflot jet, which comes with his new high position. Before departing, Dobrynin held a final meeting with Shultz -- their fourth meeting this week -- and was guest at a farewell luncheon with key senators.

Senate Democratic leader Robert C. Byrd (W.Va.), who was host at the luncheon, made public a letter to Gorbachev, which was handed to Dobrynin, recommending a Soviet-American initiative of cooperative planning and operations to combat international terrorism. Byrd sent a similar letter to Reagan.

Meanwhile, U.S. and Soviet military officials in Germany have agreed to take measures to reduce the risks of incidents such as the shooting death of Maj. Arthur D. Nicholson by a Soviet sentry in March 1985, the Defense Department announced. Among the measures are new instructions to Soviet troops in East Germany, the Pentagon statement said.

Deputy Assistant Secretary of State R. Mark Palmer, a key State Department aide on Soviet affairs, told the American Society of Newspaper Editors yesterday that Reagan has established a three-stage concept for summit meetings with Gorbachev.

The first summit, last Nov. 19-21 in Geneva, was "to establish a relationship" between U.S. and Soviet leaders, Palmer said. The second summit, to be held here this year, is "to narrow differences on really major issues" and to find a way of stating the progress in those areas. The third summit in Moscow in 1987 will be "the time to sign major treaties," according to Palmer.

The United States has "never wanted a repeat of Geneva in the second summit," said Palmer, but has hoped for substantive accomplishments in arms control, regional disputes, bilateral relations and human rights at the Washington summit.

While describing the official U.S. attitude as "a little more upbeat" as a result of Dobrynin's meetings here, Palmer said the administration feels that "we've lost five months" since the Geneva meeting because of the absence until now of productive high-level discourse.

Georgi Arbatov, director of Moscow's Institute of the U.S.A. and Canada, told the newspaper editors that "everything that happens now has something to do with" the forthcoming summit, including Thursday's underground nuclear explosion, which the Soviet Union condemned.

Arbatov complained of "rampant enmity" and "jingoism" toward the Soviet Union as manifested in such American motion pictures as "Rocky IV," "Rambo: First Blood, Part II" and "Red Dawn." The portrayal of Soviets as "the enemy," he said, is a dangerous practice that constitutes "a long stride" toward military conflict.