Behind the flurry of calls by European leaders last week for the United States to show new flexibility in arms control talks with the Soviet Union, lies a simple desire to see President Reagan erase the word "explore" from U.S. negotiator Paul Nitze's instructions and allow him to initiate proposals of his own.

A strong belief has emerged in European capitals--following Chancellor Helmut Kohl's election victory March 6-- that deployment of at least some of the 572 Pershing II and cruise missiles slated for installation in five European countries will proceed on schedule starting in December. But there also is a quest for some kind of compromise that would achieve an arms accord that would limit medium-range nuclear missiles in Europe to the lowest possible level and perhaps keep the 108 Pershing missiles--which could strike Soviet territory within 10 minutes--out of West Germany.

In that case, Bonn would probably accept an accelerated deployment of slower, less intimidating cruise missiles later this year along with Britain and Italy.

President Reagan's "zero solution," which offers to cancel the West's deployment plans if the Soviet Union dismantles its arsenal of more than 600 nuclear-tipped rockets aimed at Western Europe, is regarded as optimal but unattainable.

Last week Italy's foreign minister, Emilio Colombo, visited Reagan at the White House and told him that the Europeans would welcome a new American initiative in the stalled negotiations on medium-range nuclear missiles in Europe.

Chancellor Helmut Kohl, in an interview with The Washington Post Friday, said the time has come for a new U.S. proposal to break the deadlock in Geneva. The European pleas for a rapid shift toward a more plausible compromise are expected to reach a crescendo when Assistant Secretary of State Richard Burt consults with allied disarmament experts in Brussels this Friday.

Senior West German officials insist that Washington must change its position quickly for any arms control agreement to be achieved this year. The Kohl government now wants the United States to present new proposals rather than wait for Soviet concessions before the current Geneva negotiating round adjourns on March 28.

Secretary of Defense Caspar W. Weinberger, speaking on "Face the Nation" (CBS-WDVM) Sunday, said the United States might consider an interim agreement on medium-range missiles if the Soviets agreed to continue negotiations on "the final stage," meaning the U.S. "zero-option" proposal. "Our worry," he said, is "what is the inducement to the Soviets to come back to the table if they get an agreement that satisfies their needs and none of ours?"

Noting that "what I'd like to see first is a serious proposal from the Soviet Union in response to the serious proposal we made," he added that an interim accord could be acceptable "if the first paragraph was that immediately following the signing of this interim agreement we would reconvene to negotiate the final stage, which is zero."

In Bonn, a top government official explained that "if we want to get an agreement by October or November before the missiles arrive, we need to move right now. There are so many complicating factors, like verification matters, which require months to sort out, that we need a new American position very fast."

Part of the problem is feuding between the State Department and the Pentagon, but the crucial hindrance toward progress in the arms talks, they stressed unanimously, remains Nitze's rigid negotiating instructions that restrict him from advancing his own ideas and permit him only to "explore" Soviet proposals.

Officials in Bonn and other European capitals felt that Nitze's outline of a tentative pact, reached during his "walk in the woods" outside Geneva with his Soviet counterpart, Yuli Kvitsinsky, showed great promise before it was rejected in Moscow and Washington.

"It was certainly something we could live with," said a Foreign Ministry official here.

In the absence of any substantive shift by Washington, the West German government is now formulating its own ideas about a possible compromise, including a detailed range of missiles considered equal for both sides, that might be reached through a series of interim stages.

Government experts said there is a strong conviction that the Soviets will prove amenable to "working in stages or taking small steps" despite Moscow's rejection of the concept of partial arms control pacts.

West German officials believe that the deployment timetable and the Soviet dread of the powerful Pershing missiles will serve as the two essential forces prodding Moscow toward compromise--provided that the United States meets the Soviets halfway by offering a new proposal.

For that reason, they foresee the need to pursue deployment plans for the 108 Pershings scheduled to be stationed in West Germany later this year to keep up the pressure for Soviet concessions.

Regardless of the nature of the missiles, deployment in West Germany this year is considered a political necessity to ensure that stationing plans are fulfilled in the four other West European countries slated to receive cruise missiles.

West German acceptance of cruise missiles instead of Pershings, the government experts said, could only take place once "a final solution" in the talks was achieved because the Soviets are expected to acquire the capability to defend against the slow low-flying cruise missiles within two or three years.

Top government officials emphasized that an active search for an arms control compromise would provide a compelling defense against massive demonstrations against new nuclear missiles that are expected to take place by the summer.