Three days of talks between U.S. and Soviet officials resulted in progress on summit preparations and brought the two governments close to agreement on a visit here in mid-September by Soviet Foreign Minister Eduard Shevardnadze, State Department officials said yesterday.

The meetings late last week and yesterday with Soviet Deputy Foreign Minister Alexander Bessmertnykh reviewed "the whole range of U.S.-Soviet relations," according to State Department spokesman Bernard Kalb, who declined to characterize the outcome.

Other sources said they now expect that Shevardnadze will visit Washington to discuss summit planning and other business a few days before he speaks to the U.N. General Assembly session in New York in September.

Administration officials hope that the Shevardnadze visit, originally scheduled for mid-May but canceled by Moscow after the U.S. bombing raid on Libya in April, will lead to agreement on the next meeting between President Reagan and Soviet leader Mikhail Gorbachev.

Bessmertnykh, who was accompanied by Soviet Ambassador Yuri Dubinin and other Soviet Embassy officials, met a team led by Deputy Assistant Secretary of State Thomas W. Simons Jr. last Friday for discussion of regional issues, discussed bilateral questions Saturday with Assistant Secretary of State Rozanne L. Ridgway, and had an hour-long discussion yesterday with Secretary of State George P. Shultz.

Dubinin, who had been in Moscow, flew back to Washington for the sessions, a State Department official said.

U.S. sources cited other recent U.S.-Soviet developments as "building blocks" toward a summit meeting. They are:

A review of administrative and consular issues between the two governments, conducted in Moscow with the participation of Louis D. Sell, chief of the bilateral section of the State Department's Soviet desk.

An exchange of views on nonproliferation of nuclear weapons, which took place in Moscow with the participation of Ambassador Richard T. Kennedy, senior State Department adviser on nonproliferation.

Some movement toward agreement in the Stockholm talks on confidence-building measures in Europe and in the Geneva talks on banning the use of chemical weapons.

In the main arena of the Geneva-based nuclear and space talks, Reagan last Friday sent a letter to Gorbachev outlining in general terms the U.S. response to the most recent Soviet proposals. In addition, meetings of the U.S.-Soviet Standing Consultative Commission on compliance with prior arms agreements and of a special group to consider nuclear testing issues were convened in Geneva last week.

U.S. and Soviet diplomats are planning another set of meetings in September on the subject of Afghanistan, according to State Department officials.

Meanwhile, the administration reacted coolly yesterday to Gorbachev's announcement that about 6,000 Soviet troops will be withdrawn from Afghanistan by the end of the year. White House and State Department statements said that "if the Soviets are seriously interested in a settlement, they should present a short withdrawal timetable" at the next round of United Nations-sponsored Afghan war talks, scheduled to begin Wednesday in Geneva.

Noting that the Soviets are estimated to have 118,000 troops in Afghanistan at present, Kalb said that the "similar withdrawals" to that announced yesterday by Gorbachev had turned out in the past to be "regular rotations" of Soviet troops with no decrease in Moscow's overall force.

U.S. experts on Afghanistan said that combat activity there has seemed to be on the rise lately, rather than showing any sign of decline.

In the last round of Geneva talks, a Moscow-backed proposal for a withdrawal of Soviet forces from Afghanistan over four years was rejected by Pakistan, which proposed a Soviet withdrawal in no more than four months.