Three weeks after the shooting death of a U.S. Army major by a Soviet sentry, the Soviet Union has agreed not to permit "use of force or weapons" against American military liaison personnel in East Germany, the State Department announced yesterday.

State Department spokesman Bernard Kalb said Soviet generals also had agreed to refer the U.S. demand for an apology for the shooting of Maj. Arthur D. Nicholson Jr. and compensation for his family to "higher authority" in Moscow.

The U.S. statement followed a meeting of the top U.S. and Soviet military officers in Germany last Friday and came as a U.S. House delegation headed by Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) reported to President Reagan on its meeting in Moscow last Wednesday with the new Soviet leader, Mikhail Gorbachev.

A member of the delegation, Rep. Dan Rostenkowski (D-Ill.), quoted Gorbachev as saying that a change in the ground rules governing U.S. and Soviet military liaison officers in Germany "could very well be the outcome" of Nicholson's death and that "it should never happen again." State Department officials said additional U.S.-Soviet meetings on the military ground rules are planned.

Members of the House delegation said that Gorbachev and other Soviet officials, in extensive Moscow talks, had refused to accept responsibility for the shooting of Nicholson and maintained that the United States was to blame for his death.

O'Neill, reflecting on the four-hour session with Gorbachev last week and the White House session with Reagan yesterday, said in an interview that a summit meeting of the U.S. and Soviet leaders is unavoidable, because "both men are committed to it now."

If such a meeting occurs this year, O'Neill said, it is likely to be in or after October, by which time, he said, Gorbachev may be able to consolidate his power in the Soviet system.

A member of the House delegation that reported to Reagan yesterday quoted the president as saying "the time has clearly come" for a meeting with Gorbachev. Another lawmaker said Reagan called a meeting with Gorbachev "inevitable."

O'Neill said that, in his opinion, Reagan and Gorbachev "would understand each other" if a meeting could be arranged. He said Reagan would have to be well-prepared for such a session with the new Soviet leader, who O'Neill characterized as "having a charisma about him . . . a different style . . . a bit of class."

Interviews with participants in last week's Moscow meetings produced these details:

* The Soviets, in what some participants characterized as a significant "signal," agreed to continuing meetings on the thorny subject of human rights in the Soviet Union, among other topics.

Two U.S. lawmakers, Rep. George Miller (D-Calif.) and Marty Russo (D-Ill.), met with Vassily Trushin, first deputy minister of internal affairs, for several hours to discuss human rights. Miller said Trushin "expressed willingness to review individual cases of concern to us" and said he would report back in three or four weeks.

When human rights were first brought up in the Moscow talks, Miller said, the Soviets did not want to discuss the subject. The U.S. delegation responded that this was "unacceptable." Eventually the Soviets proposed that several working groups, including one on human rights, be established.

Miller and others cautioned that it remains to be seen whether the Soviets will make significant concessions in this area. Gorbachev, while making statements unsympathetic to the U.S. concern, said he would transmit names submitted by the House members to emigration authorities for an investigation of whether these people should be allowed to leave the Soviet Union.

* Gorbachev opened his meeting with O'Neill and three other House members with a 100-minute statement of Soviet positions on questions that had been raised by the lawmakers in earlier discussions and on Soviet policies throughout the world.

Gorbachev emphasized the importance of dialogue and peaceful coexistence as practiced in the 1970s, when U.S.-Soviet trade flourished, participants said. "We have to have the wisdom to find the development of friendliness" between the two nuclear superpowers, O'Neill quoted Gorbachev as saying.

* The new Soviet leader said he had read a 600-page report by the California-based Hoover Institution on War, Revolution and Peace suggesting that the Soviet economy faces collapse. Strongly disputing this conclusion, he said that Americans "don't appreciate the will of the Russian people" and that Americans should be more concerned about their own economic vulnerability, including large loans to the Third World countries.