Defense Secretary Caspar W. Weinberger formally invited European allies today to participate in research related to the Strategic Defense Initiative and gave them 60 days to respond.

In a letter handed out to NATO defense ministers meeting here, Weinberger asked them to indicate whether their governments are interested in participating in President Reagan's proposed $26 billion research program and to identify specific areas of technology they might contribute.

At the same session where Weinberger was trying to enlist European support for the futuristic space-based missile defense, widely known as "Star Wars," the top NATO military commander proposed a scheme for phasing out more than 1,400 aging tactical nuclear weapons based in Europe.

The plan presented by Gen. Bernard Rogers calls for reducing NATO's 6,000-weapon nuclear arsenal by the end of 1988 while modernizing the force and redistributing arms more equitably among the allied nations, according to a senior defense official.

The Rogers plan, which grew out of a 1983 NATO decision to trim its nuclear force as it prepared for new cruise and Pershing II missiles, is potentially controversial because of the resistance to adding new nuclear weapons in several European countries.

But Weinberger's offer of a European share in the Star Wars research program aroused the greatest interest at the opening session of NATO's nuclear planning group.

The invitation formalizes previously vague promises and comes as European leaders who have backed U.S. research efforts warn that moves toward a space-based defense could unleash an uncontrollable spiral in offensive and defensive weapons that would jeopardize their national interests as well as NATO's cohesion.

While Britain and France fear that antimissile defenses could render obsolete their small nuclear forces, West Germany worries about a diversion of resources from conventional forces in Europe.

Weinberger, eager to unite the allies while Congress is debating Reagan's $4.6 billion budget request for SDI research in fiscal 1986, apparently hopes to assuage European fears by offering them a piece of the lucrative project.

"Because our security is inextricably linked to that of our friends and allies," Weinberger's letter said, "we will work closely over the next several years with our allies to ensure that, in the event of any future decision to deploy defensive systems, allied as well as U.S. security against aggression would be enhanced."

A senior U.S. defense official who briefed reporters said the letter was delivered to all NATO members as well as Japan, Australia and Israel.

He said some technologies in Britain, France and West Germany are "very far advanced" and that it would be redundant for American companies to try to match them. European firms would "not be excluded" from bidding on production contracts if research succeeded and a decision was made to develop the weapons, he said.

Initial reaction from the European defense ministers was positive. Britain's Michael Heseltine said his government is "very interested" in discussing collaborative research. West Germany's Manfred Woerner said Bonn will "look closely at the mutual benefit" of such a venture.