U.S. political, military and industrial forces have begun subtly encouraging Western Europe to consider an offshoot of President Reagan's Strategic Defense Initiative (SDI) to parry shorter-range Soviet nuclear missiles.

Spearheading the loose coalition is Rep. Duncan L. Hunter (R-Calif.), a member of the House Armed Services Committee, who plans to lead a dozen lawmakers to Europe next month to promote Reagan's "Star Wars" vision -- and a more modest European defensive system based on some of the less exotic, defensive technologies being researched in the United States.

"I'm just about to strike up the band for ATBM," Hunter said in an interview this week, referring to anti-tactical ballistic missiles, a defense against the nuclear missiles aimed at Europe by the Soviet Union.

Reagan's SDI focuses largely on "strategic missiles," the ocean-spanning Soviet variety aimed at the United States.

Hunter said that in talks beginning Nov. 8 with government officials in Paris, Brussels, Copenhagen, Bonn and London he will advocate a European defense that "should basically be a NATO effort with the United States providing information and technology." Such a system could be built "in a fairly short period of time," he added, and would involve "the Europeans building it and the Europeans paying for it."

Hunter, a staunch advocate of SDI who hopes to build Allied support for the program by widening the protective shield to include Western Europe, said he envisions a European defense capable of stopping the medium-range Soviet nuclear SS20 missiles as well as shorter ranged missiles designed to carry nerve gas.

The notion of a European defense against nuclear missiles is not new; under a French initiative called Eureka, members of the European Community have discussed a common nuclear defense.

U.S. military leaders also have encouraged NATO allies to consider tactical missile defenses, most recently in a plea last week in Corlu, Turkey, by Gen. Bernard W. Rogers, NATO's commander.

The Army is particularly interested in a tactical-missile defense in Europe because it could revive the service's anti-ballistic missile program, which has been largely overshadowed by the Air Force and SDI. The Army and the LTV Aerospace and Defense Co. expect later this year to conduct a flight test of a new missile, which they contend could be used to defend Europe against Soviet warheads without resorting to nuclear or conventional explosives.

The experimental missile, called "Sure Hit" after its acronymn SRHIT (Small Radar-Homing Intercept Technology), is designed to home on the incoming warhead and destroy it by impact. A similar technology was used in LTV's antisatellite "flying tomato can" which recently destroyed a satellite in space.

One controversy underlying Reagan's SDI for the past 2 1/2 years has been the issue of whether it would extend coverage to Europe, a measure of protection that the president has guaranteed. But one State Department official said this week that sharing anti-ballistic missile technology with Western Europe could require an amendment to the 1972 Anti-Ballistic Missile Treaty.

"To assure the viability and effectiveness of this treaty," states Article 9 of the agreement, "each party undertakes not to transfer to other states, and not to deploy outside its national territory, ABM systems or their components limited by this treaty."

Assistant Defense Secretary Richard N. Perle said yesterday, however, that a European tactical-missile defense would not violate the treaty, which he said covers strategic defenses. "If they come to us" with an ATBM proposal, Perle said of the European allies, "they will find us receptive."

Kenneth L. Adelman, director of the U.S. Arms Control and Disarmament Agency, told Cable News Network this week that "I think it's a good idea" for the Europeans to pursue a tactical-missile defense and that "it's clearly allowed by the ABM Treaty."