West German Chancellor Helmut Kohl has gained President Reagan's consent to explore the possibility of an East-West summit when Kohl travels to Moscow for a four-day state visit in early July, according to West German officials.

The two leaders, who met for 45 minutes Monday at Kohl's request, agreed that West Germany's foreign minister, Hans-Dietrich Genscher, should fly to Washington immediately after the Moscow trip to inform Reagan about discussions with Soviet leader Yuri Andropov.

Reagan's approval for Kohl to probe the Russian position on a summit was reportedly coupled with the president's longstanding insistence that any such meeting must be carefully prepared so as to produce tangible results. Kohl shares this view, German officials said.

Kohl, who has advocated a superpower summit since becoming chancellor last October, emerged as a key figure at the summit of major industrialized nations by serving as a mediator who bridged differences on arms control and economic matters, according to members of several participating delegations. But his conversation with Reagan Monday indicated that important conceptual differences remain between the United States and West Germany on dealing with the Russians, German officials said.

During the summit sessions, Kohl told his fellow leaders that "making peace requires cooperation with the potential adversary," according to his spokesman, Peter Boenisch.

Kohl insisted that the West must show "continued flexibility in arms control talks on all levels and, in particular, must explore all possibilities to reach an agreement in Geneva" that would restrict medium-range nuclear weapons in Europe, said Boenisch.

Reagan in recent interviews has voiced an increasingly stern view that deployment is probably the only way to convince the Soviets to negotiate seriously. Kohl's view is that the rationale must be to negotiate to prevent or restrict deployment.

With his country bracing for trouble over the controversial deployment of Pershing II missiles later this year if arms talks in Geneva fail, Kohl came to Williamsburg intent on minimizing any potential conflict among the allies and on making sure that Reagan would be responsive to any signs of Russian willingness to negotiate at Geneva or to agree to a U.S.-Soviet summit, German officials said last week.

One emerging area of difference centers on Kohl's sensitivity to the continuing division of Germany. Recent warnings from Moscow that Russian missiles may be stationed in East Germany or other Warsaw Pact countries could intensify political anxieties in Bonn, while provoking increasingly sharp responses from Washington.

There are also strong indications that the West Germans, while publicly professing willingness to deploy 108 of the powerful Pershing IIs, would prefer to station the less intimidating, slower cruise missiles if an arms pact could be reached this year.

Conference sources gave this account of summit deliberations:

In hours of wrangling Sunday over the wording of a statement endorsing deployment unless the Soviets compromise over medium-range missiles in Europe, Kohl acted as mediator between Canada's Pierre Trudeau and Britain's Margaret Thatcher.

Trudeau argued fervently for the need to stress the West's dedication to peace while Thatcher insisted on a firm display of allied will to station the new missiles, if no progress is reached in Geneva, to send a tough message to Moscow.

Playing the role of pragmatic consensus seeker, Kohl led the search for phrasing that would incorporate conciliatory hopes for peace with a commitment to deploy the missiles if the Soviets did not bend in arms control talks.

Kohl also helped strike a balance between France and the United States on the need for a new conference to revamp the international monetary system established at Bretton Woods in 1944.

The United States has shown little enthusiasm for the idea, broached recently by French President Francois Mitterrand.

Kohl met with Mitterrand over breakfast Monday and promised to do what he could to promote future consideration of the French plan.

In the end, Kohl persuaded Reagan to accede to a study that would explore the prospects of such a conference. A French delegate said later that "thanks to Kohl, we got more than we expected."

In contrast to his more irascible predecessor, Helmut Schmidt, Kohl prides himself on his ability to work in congenial fashion with Reagan, who shares an aversion for petty feuds.

Kohl often reassures audiences that his country is firmly rooted in the Atlantic Alliance. He frequently employs the phrase "we are not wanderers between two worlds" to debunk the idea that West Germany is drifting inexorably toward neutralism.

At a press conference Monday, Kohl insisted that on his forthcoming trip to Moscow he would confront Andropov as a staunch backer of the alliance, and would tell him that Soviet efforts to split West Germany from the western alliance through a "carrot and stick" policy would not succeed.

Despite such loyal proclamations, Kohl recognizes that West Germany maintains distinct national interests, such as the importance of family ties and cultural channels with East Germany, that demand obeisance to detente.

His trip to Moscow, as the first Western leader to pay an official visit since Andropov assumed power, reflects his view that "personal contacts with the Soviet leadership remain very important to us," said Boenisch.

When the summit opened, Kohl joined with Mitterrand in opposing the idea of a statement on arms control since the purpose of the meeting was to examine global economic problems.

Once it was decided, however, that the nuclear issue was too important to dismiss at a gathering of western leaders, Kohl sought to find the balance between western commitment to proceed with nuclear rearmament and an earnest desire to pursue compromises.

Kohl's aides said the most troublesome issue was a phrase in the statement that said "negotiations will determine the level of deployment."