The Soviet Union yesterday challenged the accuracy of an official American statement last week that the Soviets had pledged not to use force against U.S. military liaison personnel in East Germany.

The statement, distributed late yesterday by the Soviet Embassy here, reignited the bitter controversy about the shooting death last month of a U.S. Army major after a high-level U.S.-Soviet military meeting and a now-challenged U.S. report on that meeting seemed to suggest its resolution.

The State Department responded almost immediately to yesterday's Soviet Embassy statement by summoning a senior embassy official to reject the Soviet interpretation as "unacceptable" and contrary to fact.

State Department sources said they were puzzled and taken aback by the unexpected Soviet blast, and speculated that it arose from differences between military and civilian authorities in Moscow.

Similar differences about the handling of the case have emerged in Washington. Here the Defense Department has been more demanding than the State Department and some officials in the White House in insisting on a Soviet apology for the shooting of Maj. Arthur D. Nicholson Jr. by a Soviet sentry as well as compensation for Nicholson's family.

In the latest manifestation of its tough position, the Pentagon announced yesterday before the Soviet statement was issued that a planned trip to the Soviet Union set to begin last Saturday by 15 officers from the National War College has been cancelled because of "the lack of Soviet responsiveness in meeting our demands for an apology and compensation."

The War College trip had been considered a U.S. breakthrough, in view of past difficulties about such visits and initial Soviet rejection this year of the planned journey by senior military officers studying at the service school at Fort McNair here.

The March 24 killing of Nicholson, a U.S. military liaison officer in Soviet-controlled East Germany, created tension and ill-will in American-Soviet relations at a time when the top leaders on both sides seemed to be heading toward a summit meeting.

President Reagan, taking a low-key approach, said the killing only increased his desire to meet the new Soviet leader, Mikhail Gorbachev. A March 30 meeting of Secretary of State George P. Shultz and Soviet Ambassador Anatoliy Dobyrnin set the stage for high-level military meetings intended to resolve the case.

The upshot was an April 12 meeting near Potsdam, East Germany, of Gen. Glenn K. Otis, commander of U.S. Army Europe, and his Soviet counterpart, Gen. Mikhail M. Zaytzev.

The State Department, reporting on this session last Tuesday, said, "We obtained agreement from the Soviets that they will not permit use of force or weapons against the members of our military liaison mission in the future." The department also said that the Soviets "agreed to refer our demand for an apology and compensation for the Nicholson family to higher authority."

Repeating this report yesterday, State Department officials said there is "no doubt" that the Soviet general promised not to use force in the future against U.S. liaison personnel, and that Zaytzev told Otis that instructions were being issued to reiterate this point to Soviet personnel in his command.

The officials reported Zaytzev as saying he could not deal with the U.S. demand for an apology and compensation, but would have to report it to higher authority. Subsequently, officials said, the U.S. demands have been taken up with the Soviets through diplomatic rather than military channels.

Yesterday's Soviet Embassy statement charged that last week's State Department statement "presents in a distorted light the content and results of the meeting between the military representatives of the two countries."

The embassy statement went on to say, "The assertion that the Soviet allegedly agreed to consider some kind of compensation in connection with the incident and renounced the right to take legitimate steps provided for by the military manuals does not correspond to the facts."

Insisting, as Moscow has throughout, that the United States bears the responsibility for Nicholson's death, the embassy statement insisted that "the actions of the Soviet sentry were completely lawful. They were not taken against a member of the U.S. military mission as such, but against an unknown intruder who was carrying out an intelligence mission and did not comply with the warnings of the sentry, who was acting in strict conformity with the military manuals."

Nicholson and his driver, Sgt. Jessie Schatz, were described by the United States as carrying out routine activities of the U.S. and Soviet liaison missions, which have functioned in each others' military zones in Germany since 1947.

The State and Defense departments have rejected Soviet accusations that Nicholson was in a restricted military zone when he was killed. In any case there was no reason for the use of force, especially lethal force, U.S. statements have said.

Surveillance activities, sometimes described as "licensed espionage," are the principal and well-accepted function of special American and Soviet military missions in Germany, according to U.S. officials. Until the Nicholson case, the ground rules under which the teams operated had permitted hassling of the liaison officers but not the use of lethal force.

The House of Representatives, meanwhile, passed yesterday, 394 to 2, with Reps. George W. Crockett Jr. (D-Mich.) and Gus Savage (D-Ill.) dissenting, a resolution condemning the Soviet Union for the "murder" of Nicholson as "clearly inconsistent" with the 1947 U.S.-Soviet agreement.