President Carter underscored American backing for Yugoslavia's independence yesterday by saying the United States will "do what it must to provide that support."

In a statement issued after the death of President Tito, Carter praised the late Yugoslav leader's "resolute determination" to maintain his country's neutrality.

"For more than three decades, under administrations of both parties, it has been the policy of the United States to support the independence, territorial integrity and unity of Yugoslavia. President Tito's death comes at a particularly troubled time in international relations.

"I reaffirm today that America will continue its longstanding policy of support for Yugoslavia and do what it must to provide that support," Carter said.

The president also halted Tito as a "towering figure on the world stage" and expressed confidence in the new Yugoslav leadership's ability to "lead the nation and its economy through this period." He also pledged that the administration "will not tolerate" any terrorist acts mounted by anti-Tito exile groups "against Yugoslavia or its representatives here."

Since Tito fell ill in January, various Yugoslav exile groups here and in other Western countries have become increasingly active anticipating internal turmoil in Yugoslavia after Tito's death. The most active are Croatian exiles, including some groups that have openly advocated ties with the Soviet Union to win independence for Croatia, one of Yugoslavia's six constituent republics.

Since Tito's rift with Joseph Stalin in 1948, the United States has extended more than $4 billion in various forms of aid to support Yugoslavia's independence and deny the Soviets access to the strategically located Balkan country.

In Moscow, the Soviet news agency Tass saluted Tito as a "prominent leader of the world communist movement" and said the "Soviet people deeply grieve" at his death. Tass made no mention of Yuglslavia's defection from the Soviet Bloc but instead emphasized Tito's "services in the common struggle against fascism and in the development and strengthening of fraternal friendship and all-around cooperation" between the two countries.

The Yugoslavs have vigorously condemned the Soviet invasion of Afghanistan and Moscow-Belgrade relations have suffered as a result. The Soviets, in turn, have assailed the new Yugoslav leaders, saying some among them were pursuing an anti-Soviet course.

Meanwhile condolences from around the world poured into Belgrade including those of French President Valery Giscard d'Estaing, who hailed Tito for "being able to preserve the liberty and independence of his country" and becoming "the authentic voice of nonalignment."

Tito, who along with India's Jawaharial Nehru and Egypt's Gamal Abdel Nasser was the founder of the nonaligned movement, last year defended their original principles at Havana's nonaligned summit against attempts by more radical countries led by Cuban President Fidel Castro that wanted to tilt the movement toward the Soviet Bloc.

Egypt's President Anwar Sadat is Cairo called Tito a "dear friend and comrade in arms along the road of struggle for the establishment of peace and justice in the world." Egypt announced a week of official mourning for Tito.

In Bonn, former chancellor Willy Brandt said "the whole of mankind is the poorer" after the death of the farsighted and brave pioneer of peaceful coexistence."