The first summit meeting between American and Soviet leaders in six years has awakened fresh hopes among U.S. allies that Washington and Moscow may now be groping toward tangible improvements in the East-West climate after the collapse of detente bred a phase of dangerous tensions.

The rapid consolidation of power by Mikhail Gorbachev within eight months of assuming the Soviet leadership has buoyed hopes that the Kremlin is now controlled by a man driven by the need to modernize his nation and to do so by nurturing a more stable relationship with its chief foreign rival.

The coincidence of Ronald Reagan's second presidential term, following four years of rebuilding American power and prestige, has convinced many allies that he will focus the rest of his tenure on burnishing his historical credentials as a peacemaker.

Now that Reagan finally has a vigorous counterpart in Moscow who shares his concern about public image, the allies feel that both leaders may be motivated to act in ways more keenly attuned to a global yearning for civil dialogue between the superpowers.

The Reagan administration's awareness that it faces a more formidable contest for hearts and minds in the Gorbachev era has been reflected in requent consultations with the allies prior to the summit meeting. Besides Reagan's meeting with five leaders of industrialized democracies in New York last month, North Atlantic Treaty Organization foreign and defense ministers have held separate sessions in Brussels to ensure that Reagan goes to Geneva with the full support and solidarity of the allies.

Reagan's quick response to the Soviet proposal that would cut strategic nuclear weapons by 50 percent was greeted with approval and relief in European capitals. In New York, western leaders had warned Reagan about letting Gorbachev set the pace for the summit with his wide-ranging offer, and they were reassured that the United States had seized the upper hand on arms control by diverting attention from Moscow's proposal.

The common desire among western nations and Japan to see the summit talks instill more predictability and understanding in the Soviet-American dialogue has inspired them to submerge apprehensions about Reagan's vision of a space-based missile defense and the influence of Pentagon hawks who doubt the worth of arms control.

Instead, the allies have displayed a striking consensus, at least publicly, behind the U.S. administration's tactics and priorities in its approach to the Geneva summit.

Concerned about the political risks of a disappointing outcome, the allies have joined the United States in seeking to lower public expectations that the meeting might lead to a conceptual breakthrough that could set guidelines for an early accord at the Geneva negotiations on nuclear and space weapons.

"I am being prudent about what I expect," Italian Prime Minister Bettino Craxi told parliament, expressing sentiments of other leading Europeans. "I do not wholly discount an agreement, and I would consider a breakdown injurious. I think it would already be a great result if the summit effectively opened up a period of dialogue, if it created a different atmosphere of greater mutual trust."

In West Germany, Chancellor Helmut Kohl has acclaimed the fact that the summit is taking place as a vindication of his repeated pleas for more intensive East-West contacts. Although Kohl, too, has sought to minimize the stakes at Geneva, his advisers say he is acutely aware that Bonn's hopes for closer relations with East Germany depend to a large extent on the evolution of U.S.-Soviet ties.

Senior Foreign Ministry officials in Bonn said the Kohl government is more convinced than ever that it must work through Moscow to enhance contacts with East German authorities because their room for maneuver has been greatly circumscribed by the emergence of a dominant Gorbachev after a succession of ailing Soviet leaders.

Like British Prime Minister Margaret Thatcher, Kohl is eager to show that his friendly rapport with fellow conservative Reagan can have an impact on U.S. policy and bring to bear Europe's desire for further relaxation of tensions with Moscow.

Britain and West Germany also share a particular interest in promoting an East-West agreement to reduce chemical weapons stocks in Europe. Officials in both countries believe that Reagan and Gorbachev might be able to make more substantial headway in that area rather than in forging a deal on nuclear weapons.

"They are not going to get a settlement" on nuclear arms, predicted a British official who closely reflects Thatcher's thinking. What Britain seeks, he added, is "a real impetus to the arms-control process: the object is to break the logjam."

If nothing else, Britain and other allies would applaud a bilateral deal on consular or cultural exchanges or a joint agreement for regular high-level meetings between the superpowers. "If that's all it does, it would be a slightly disappointing but worthwhile end," said a Foreign Office diplomat in London.

France, which last month hosted Gorbachev's first visit to the West as Soviet leader, has kept its distance before the summit to underscore its independent foreign policy. President Francois Mitterrand rebuffed Reagan's invitation to huddle with him and other allied leaders in New York last month.

"We have already had our own summit with Gorbachev," explained Dominique Moisi, associate director of the French Institute for International Relations. "There is general indifference among public opinion about what is seen as another media event. We fear little and hope for little."

Political analysts cited another reason for French aloofness as that government's determination not to give Moscow an excuse to include the French force de frappe in the overall western nuclear arsenal at the Geneva arms negotiations. Paris has countered this longstanding Soviet demand by insisting its nuclear force remains truly autonomous.

Japan has also kept a low profile but shares the wishes of other allies that the Reagan-Gorbachev meeting will improve prospects for better diplomatic ties with Moscow. Japan's specific interest, as emphasized to Reagan by Prime Minister Yasuhiro Nakasone in New York, is that any arms pact limiting medium-range missiles must not permit the Soviets to move SS20 rockets from the European to the Asian theater.

While the allies acknowledge that public interest is so great that arms control is bound to dominate the agenda, they have supported U.S. intentions to raise other issues such as human rights and regional conflicts.

An exchange of views on regional conflicts, such as Afghanistan, the Middle East or southern Africa, is not likely to yield much progress, according to officials in various European capitals.

The probable result, a British diplomat said, is "a pretty unproductive discussion in which the two sides are talking over each other's shoulders."