President Carter arrived here tonight after serving notice that he will press for a renewed show of opposition to the Soviet invasion of Afghanistan in the summit meeting with allied leaders beginning Sunday in Venice.

In a statement at the White House before leaving on a week-long trip to Europe, Carter placed Afghanistan at the top of what amounted to his personal agenda for the two-day Venice economic summit conference.

"I will be totally frank with you, as I will be with them," the president said of his upcoming talks with the allies. "The industrial democracies are being tested. Let there be no misunderstanding about this anywhere in the world. We are not motivated by hostility, or by any desire for reckless confrontation or a return to the cold war. But we must sustain world opposition to Soviet aggression, and not allow the Soviets to derive any permanent benefits from their invasion of a neutral nation."

Carter's plane landed at Rome's Ciampino Airport late tonight, and the president then flew immediately by helicopter to Quirinale Palace atop Rome's highest hill, which was once a summer residence for the popes and will be Carter's home for the next two nights.

Bathed in bright television lighting, the president, his wife, Rosalynn, and daughter, Amy, were greeted warmly by Italian President Sandro Pertini as they stepped onto a cobblestoned helipad outside the 16th century palace.

While Amy clutched a stuffed toy lion, Carter grinned broadly throughout the brief welcoming ceremony, which included a two-minute walk in review past the colorfully-uniformed palace guard in the building's formal reception room.

The president, in delivering his statement on Afghanistan, slightly altered and softened a prepared text of his departure remarks. But White House officials traveling with him said the changes were not significant and that Carter stood behind the importance the statement attached to the Afghanistan issue.

Officials also said they expect no serious dispute at the Venice summit between the president and West German Chancellor Helmut Schmidt about the question of deploying medium-range nuclear weapons in Western Europe.

This assessment by White House Press Secretary Jody Powell and Secretary of State Edmund S. Muskie will get an early test Saturday night in Venice, when Carter has scheduled a private meeting with Schmidt before the formal opening of the summit Sunday.

Schmidt will meet Soviet President Leonid Brezhnev June 30 in Moscow, and there has been some concern that he would propose a freeze on the development of such weapons. Carter and Schmidt have exchanged letters on the issue, reviving long-standing reports of personal animosity between the two men.

Muskie, however, told reporters today that Schmidt "insists he still supports" the missiles deployment. "Apparently there has been some rhetoric that there is a change," Muskie said. "I would expect that when it's talked out there will continue to be agreement."

The president's European journey, which next week will include visits to Yugoslavia, Spain and Portugal, will begin officially Friday when he meets here with Pertini and Italian Prime Minister Francesco Cossiga. He is also scheduled to meet with Pope John Paul II on a Saturday at the Vatican.

Carter's two days in Rome will be a prelude to the centerpiece of the trip, the Venice summit conference of the leaders of the United States, Britain, France, West Germany, Italy, Japan and Canada.

The Venice gathering will be the sixth in a series of yearly summits on world economic issues and the fourth that Carter has attended. It comes at a time of new strain between the United States and some of the European nations over such issues as the Soviet invasion of Afghanistan, the continuing stalemate over the American hostages in Iran and the Middle East peace process.

The president's attempt to lead retaliatory steps against the Soviet Union, such as the boycott of the Moscow Olympics, has produced only mixed results among the allies. Nor is the administration totally satisfied with the degree of pressure the Western Europeans have imposed on Iran in an effort to win the release of the hostages.

The Western Europeans, in turn, were shaken by the secret and aborted Iranian rescue raid and are openly worried about the impact on Western Europe of the renewed tension between the Soviet Union and the United States since the Afghanistan invasion.

At their own meeting in Venice last week, the nine nations of the European Common Market demonstrated their growing independence and doubts over American foreign policy by declaring their intention to explore the possibility of a new Middle East peace initiative with the Palestine Liberation Organization and other Arab parties.

The European leaders were careful to say they did not intend to interfere with the American peace initiative begun by the Camp David accords, but their Venice declaration also reflected doubt that the Camp David process would succeed.

All of these issues, which could push the economic topics to be discussed at the Venice summit into the background, were mentioned by Carter in his statement before departure.

"While short in time, our trip is long in difficulty," he said, and acknowledged that among the subjects to be discussed by the summit participants will be "individual differences among our nations."

The president said that in seeking a united response to the Soviet invasion of Afghanistan and in discussing other issues, the United States "will be clear both in voicing our needs and in understanding other voices."

"We are not the Warsaw Pact, held together by one nation's tanks," he continued. "We are bound by shared ideals, shared goals and shared respect. Our alliance is based on understanding, not demands, on listening to each other's concerns, not dictating terms."