The United States and Italy called today for a unified Western response to the Soviet Union's invasion of Afghanistan as President Carter warned against the "false belief" that Western Europe can be "an island of detente."

In a joint statement issued near the end of the president's state visit to Italy, the two governments declared that they view "as indispensable a comprehensive Western political strategy designed to make clear to the Soviet Union by application of tangible measures the necessity of a prompt and complete withdrawal of its troops from Afghanistan."

Tonight, delivering a toast at a state dinner hosted by Italian President Sandro Pertini, Carter continued to emphasize the importance of Afghanistan, which he clearly intends to make a central theme of his week-long visit to Europe.

"It is our responsibility to register in concrete terms our condemnation of the Soviet invasion for as long as that invasion continues," he said.

"Above all, everyone must know that efforts cannot succeed to divide our alliance or to lull us into a false belief that somehow America or Europe can be an island of detente while aggression is carried out elsewhere," he added.

The reference to an "island of detente" was clearly directed at Western European leaders, who, living in the shadow of the Warsaw Pact's military power, are wary of Soviet-American tension over Afghanistan and reluctant to go along fully with Carter's call for concrete response.

The president is also certain to raise this issue anew beginning Sunday, when he meets in Venice with the leaders of the United States' principal allies from Western Europe, Japan and Canada for a two-day economic summit conference.

Neither the joint statement issued at the conclusion of Carter's talks with Petini and Italian Prime Minister Francesco Cossiga, nor the president's toast tonight, mentioned specific steps in response to the Soviet invasion.

White House Press Secretary Jody Powell said Carter is not going to the Venice summit with new, specific proposals for the allies to take against the Soviets. But he said the president reiterated to Pertini and Cossiga the American position that while "some of our allies have supported us [and] some have not, we will stand resolute."

Another administration official, conceding that there is no prospect for a withdrawal of Soviet troops from Afghanistan in the near future, said Carter's statement was intended to give "a sense of direction" to the allies in dealing with the Soviets.

Carter's role as leader of the Western alliance, important not only to American foreign policy but to the president's domestic political standing will be under close scrutiny at the Venice summit.

Still plagued in Europe by criticism that he is often weak and vacillating, Carter would like nothing better than to be seen at Venice as the dominant figure, pulling the others in his direction.

But there are bound to be disagreements at Venice and, anticipating them, the president tonight referred to the criticism of allied relations under his leadership in the kind of optimistic tones he has recently been applying to U.S. domestic problems.

"Some voices in my country and Europe talk about disarray," he said. "Some pessimists view debate among democratic nations as a signal of fatal weakness. . . .

"Our experience and reality itself shows clearly that these self-styled 'realists' are wrong. Open and public grappling with economic or social problems cannot obscure the extraordinary achievements of our society as a whole."

Carter began the day with a meeting with Pertini and later in the morning met with Cossiga. He described these sessions as "excellent talks -- very fruitful, very thorough, very friendly, very constructive." After a ceremonial wreath-laying at the Tomb of the Unknown Soldier at Rome's Victor Emanuel monument, the president, his wife, Rosalynn, and daughter, Amy, spent the afternoon as have thousands of American tourists -- seeing the sights of ancient Rome.

The Carters were given a private tour of the Roman Forum and Coloseum, which the president described as "thrilling, beauttiful, exciting, unbelievable."

As the presidential party moved through the city, Carter was greeted by polite applause from modest crowds as most of cosmopolitan Rome went about its daily business. Some 7,000 Italian police and military personnel were on hand for secuity, but despite Italy's continuing problems with terrorism, the security forces were less prevalent than in many other world capitals the president has visited.

There are no major, outstanding issues between the United States and Italy and this was evident in the relaxed tone of the Carter visit. The joint statement called for the release of the American hostages in Iran and for the deployment of theater nuclear weapons in Western Europe and downplayed differences between the United States and its European allies over the Middle East peace process.

The two governments also announced agreement to cooperate in designing a major solar power facility in Puglia, in southeast Italy.