Soviet President Yuri Andropov has proposed that the Geneva negotiating sessions on medium-range missiles in Europe should be extended to improve chances for a compromise this year, the West German government announced today.

In a new hint of Soviet flexibility, Andropov told Chancellor Helmut Kohl in Moscow this week that the current round of Geneva talks should proceed a week beyond the July 15 recess and resume a week early on Sept. 8, according to Bonn spokesman Peter Boenisch, speaking at a press conference here.

In March, President Reagan made a similar proposal that the then- adjourned talks resume earlier than scheduled. The Soviets took up the suggestion and the opening of the round was moved up several weeks, to May 17.

Kohl's four-day visit to the Soviet Union has received mixed reviews in the West German press. Some newspapers lauded his candor in stressing West Germany's commitment to deploy new missiles if arms talks fail, while others denounced his comments as too rigid and undiplomatic.

Former chancellor Willy Brandt, the party chairman of the opposition Social Democrats, described the trip as "unusually unproductive" and said he was "embarrassed by fatuous claims that business will continue to flourish even if we take a step nearer the edge of catastrophe."

Kohl's espousal of German reunification by peaceful means during his press conference in Moscow, which purportedly shocked Soviet officials, also raised a storm of controversy between those who applauded his guilt-free patriotism and others who felt he antagonized Soviet sensitivities on the subject.

His revelation about asking Andropov how he would act if his capital and fatherland were divided elicited a torrent of favorable telegrams from Germans supporting Kohl in his implied effort to distance West Germany from the wartime past and seek common treatment.

During three hours of talks with Andropov on Tuesday, Kohl claims to have detected signs of Soviet willingness to break the stalemate in Geneva and to enhance the East-West dialogue.

Senior aides to the chancellor said the Soviet leader's expressed desire to meet with President Reagan at a well-prepared summit and his refusal to rule out further arms control talks after deployment represent positive indications that Moscow wishes to repair its relations with the West.

"We think the Soviets have not yet decided what to do if deployment take place," said a top foreign policy adviser. "We were pleased to see that Andropov believes there is still a serious chance to reach an agreement this year."

Sources in Kohl's delegation reported Tuesday that Andropov broadly hinted that the Soviets would retaliate for the NATO deployment by installing new rockets in Eastern Europe, a prospect also suggested in his May 3 speech honoring East German leader Erich Honecker.

Kohl shared his impressions of the trip today by telephone with British Prime Minister Margaret Thatcher. He also plans to see French President Francois Mitterrand later this month to discuss East-West relations.

Foreign Minister Hans-Dietrich Genscher will travel to Washington Sunday to brief President Reagan and Secretary of State George P. Shultz on the meetings with Andropov.

A senior Kohl adviser said that while the Bonn government supports the western consensus that British and French nuclear missiles should not be included in U.S.-Soviet talks on medium-range nuclear weapons, some kind of initiative may be necessary to break the deadlock and ease Soviet demands that such deterrent systems must be counted.

"We cannot pretend that the British and French missiles simply do not exist," he said.

One possible suggestion raised in Bonn would involve seeking an interim solution, possibly along the lines of the so-called "walk in the woods" formula devised by U.S. and Soviet negotiators last summer, and incorporating the French and British systems in "the extended scope" of strategic arms reduction talks also taking place in Geneva.

During a walk in the woods near Geneva last July, U.S. negotiator Paul Nitze and his Soviet counterpart, Yuli Kvitsinksi, reached tentative agreement on a compromise that would limit the United States to 75 cruise missile launchers, each with four cruise missiles, and the Soviet Union to 75 triple-warhead SS20 missiles.

Moscow and Washington rejected the package, but it has frequently been cited as the most promising formula to break the current stalemate.

A senior West German official said today that Kohl raised the formula in his discussions with Andropov but that he received only a noncomittal response.

Rep. Thomas J. Downey (D-N.Y.) quoted Soviet Marshal Sergei Akhromeev, first deputy chief of the Soviet general staff, yesterday as saying that if the proposal "is offered again, it would be negotiated."

Rep. Dick Cheney (R-Wyo.), though not disputing the accuracy of Downey's remarks, said he had come away from the talks "with a slightly different impression." He added that the marshal had not commented "on the merits" of the Nitze-Kvitsinsky concept.

Another possible way out of the impasse might be to include the French and British systems within the forum of a European disarmament conference scheduled to begin early next year in Stockholm.

But the adviser to Kohl said there were no firm signs that the Soviets were prepared to accept such alternative ideas, nor, for that matter, did Kohl glean any indication that the Soviets were now willing to destroy part of their SS20 arsenal.

"We do not want to see the Soviet rockets put into boxes or moved to Asia," he said. "They must be destroyed."