US, Soviet leaders maneuver for edge in upcoming talks.

The pre-Geneva battle for the hearts and minds of the Western European allies is in full swing on both sides of the Atlantic. The subject is space-based military systems, and the heavy hitters are out in force.

Mikhail Gorbachev, the Kremlin's No. 2 man, has just finishing wowing them in London. Soviet Foreign Minister Andrei Gromyko is going to Rome soon. And Soviet President Konstantin Chernenko wants to meet with French leaders in March. In all of this diplomatic activity aimed at the Western alliance, the Soviets are stressing the importance of heading off an arms race in space, particularly the Reagan administration's push for advanced antisatellite and antimissile systems.

British Prime Minister Margaret Thatcher arrives in Washington Saturday for talks with United States officials that are sure to reflect European wariness about the President's Strategic Defense Initiative (SDI). And yesterday, US Defense Secretary Caspar Weinberger gave a major address to foreign journalists explaining the rationale behind the ''star wars'' program.

All of this is reminiscent of the US-Soviet struggle two years ago over deployment of US-built Pershing and cruise missiles in NATO countries. Moscow's attempts to upset Western alliance unity on the issue and influence the West German election failed in that case. But Washington has not had an easy time keeping the alliance together (particularly Belgium and the Netherlands) on deploying NATO's new nuclear missiles.

In his speech Wednesday, Mr. Weinberger stressed the importance to individual allies, and the alliance as a whole, of US missile defense goals. He argued that nuclear stability could be increased and that even attacks with conventional missiles could be deterred by such a system. If nuclear forces are reduced to much lower levels, he said, strategic defense could help alleviate compliance verification problems.

Weinberger pointed out that the strategic arms limitation and antiballistic- missile treaties negotiated in the 1970s have not significantly limited the Soviet offensive nuclear buildup. And he asserted that, since the signing of the Anti-Ballistic Missile Treaty 12 years ago, the Soviets actually have spent more on strategic defense (including defense against bombers) than on offensive systems.

This is the first time a Cabinet-level official has so strongly and in such detail made the case for SDI, particularly with a European audience in mind. Administration officials say the decision to have Weinberger make such a speech came immediately after the November election. And they acknowledge that the timing - close, but not too close, to the US-Soviet meeting in Geneva in early January - is viewed as very important here.

The speech (given at the Foreign Press Center in Washington and broadcast live to a similar facility in Los Angeles) was videotaped, made available to overseas broadcasters, and immediately requested by 14 countries. It follows a series of private briefings for European defense experts in which US officials say they have begun to build support for their position.

But officials here acknowledge that convincing the Europeans, whose anxieties over ''star wars'' remain acute, is an uphill fight. ''It's natural, since this is so new to them,'' a senior administration official said.

The Reagan administration is well aware of the domestic political ramifications of the Weinberger address, which was carefully scrutinized in advance by the White House. Congress will be asked to approve $3.8 billion for strategic defense research next fiscal year, doubling this year's figure. And there have been recent sharp criticisms of space-based missile defense by important American figures who are well regarded here and abroad.

In an article in the current issue of Foreign Affairs, McGeorge Bundy, George Kennan, Robert McNamara, and Gerard Smith detail their opposition to ''star wars.'' (This same so-called ''gang of four'' caused a considerable stir two years ago when they urged NATO to adopt a no-first-use policy on nuclear weapons.)

And, in a lengthy paper last week, former US Defense Secretary Harold Brown, a scientist who has worked on missile defense for more than 30 years, detailed why he thinks such a system would be both ineffective and dangerous.

''It would be wrong to consider this (Weinberger's) speech an answer to the (Foreign Affairs) article,'' said a senior Pentagon official. ''But it does address that article and many of the themes in Harold Brown's paper.''