Soviet President Leonid I. Brezhnev has complained to President Carter and West European leaders abou the West's delay in responding to his willingness to negotiate reductions in medium-range nuclear missiles.

U.S. sources said yesterday that Brezhnev's complaint was contained in letters sent Friday to Carter and the heads of governments allied with the United States in the North Atlantic Treaty Organization.

In the letter, the sources said, Brezhnev reiterated his offer, made to West German Chancellor Helmut Schmidt in Moscow at the beginning of July, to begin discussions on western proposals for limiting so-called theater nuclear forces within Europe.

This new Soviet more was one of the principal topics discussed in a meeting late yesterday between Secretary of State Edmund S. Muskie and West German Foreign Minister Hans-Dietrich Genscher. Genscher stopped here for the meeting while en route to the United Nations to deliver a speech today.

The two subsequently issued a joint statement saying they had "discussed the preparations for preliminary exchanges between the United States and the Soviet Union on theater nuclear forces which in their view are expected to occur at an early date."

However, in response to questions during a brief appearance before reporters, the two refused to elaborate on what the term "early date" means. "That statement says all it is meant to say at this point," Muskie said.

Earlier yesterday, State Department spokesman John Trattner denied suggestions that the United States and its NATO allies are delaying in picking up on Brezhnev's response to what originally was a NATO proposal. Trattner said: "We are moving with deliberation but speed in consulting with our allies. We are not in a delaying mode."

However, reliable sources said privately, the United States and its NATO partners are in no immediate rush to move ahead with the Brezhnev offer because of a number of domestic and alliance-wide problems. As a result, the sources added, Brezhnev is justified in charging that the West is stalling.

The principal problem from an American point of view, the sources said, is Carter's reluctance to enter into major new arms negotiations while in the midst of a reelection campaign. According to the sources, the U.S. preference is to defer action until after the Nov. 4 election.

In addition, Western leaders are understood to believe that engaging the Soviets in discussions at this time might jeopardize hopes of stationing medium-range missiles in Belgium, a NATO country that has delayed until September a decision on whether to accept the missiles.

Strong political forces in Belgium are opposed to deployment of the weapons there, and have argued that NATO should seek to negotiate nuclear arms reductions with the Soviet-led Warsaw Pact.

The belief in western alliance circles, is that raising expectations of such negotiations at this point could tip the decisions in Belgium against accepting the missiles.

At a ministerial meeting in Brussels Dec, 12, NATO agreed to deploy U.S. Tomahawk and new-generation Pershing missiles in West European bases, from where they would be able to strike deep inside the Soviet Union. These weapons, whose deployment is to begin in 1983, are intended to balance new Soviet 2,500-mile range SS20 mobile missiles, already in place, and scores of new Soviet Backfire bombers. m

The decisions was extremely sensitive politically in a number of NATO countries such as Belgium, in part because of a Soviet campaign of conciliatory gestures and threats designed to put pressure on the European allies not to go along.

To relieve the pressure, NATO coupled its missile-deployment decision with an offer to open talks between the United States and the Soviet Union on limiting use of the missiles.

The NATO plan, conveyed to the Soviets by Muskie's predecessor, Cyrus R. Vance, said limiteds on U.S. medium-range missles should be accompanied by similar Soviet limitations, that the negotiations should be between Washington and Moscow within the extent of the strategic arms limitation treated (SALT) talks, and that their objective should be to limit landbased missile systems in Western and Eastern Europe.

On Jan 3. the Soviets, through their embassy here, official rejected the NATO offer and said there could be no arms limitation talks unless NATO publicly abandoned its plan to deploy the Tomahawks and plan to deploy the Tomahawks and Pershings in Western Europe.

However, the Soviets shifted position when Schmidt went to Moscow at the beginning of July. At that time, Bezhnev dropped the Soviet demand that NATO give up is missile-deployment plan and said his government was willing to enter into preliminary talks on arms reductions.

Last month, Deputy Secretary of State Warren M. Christopher, in a briefing for NATO ambassadors, said both sides were approaching the proposed talks with flexibility. Christopher noted the although the Soviets nuclear weapons deployed in the European theater on American ships, planes and submarines, the United States did not interpret that as a condition of negotiations.

In his briefing, Christopher conceded that the United States is interested primarily in discussing land-based medium-range missiles, but he added that this also was not a condition.

However, in the almost two months since Brezhnev made his offer the West has not responded except to talk vaguely about consultations, within the alliance on what to do about the Soviet proposal. That apparently prompted Brezhnev's complaint about stalling, and put NATO in the odd position of appearing to be holding back on a negotiating initiative it had originated.