VENICE, JUNE 4 -- President Reagan will try to rescue his damaged reputation for leadership at home by attempting to show that he can still function as an effective performer on the world stage, according to White House officials.

"It's not morning anymore, but it's not the twilight of the Reagan presidency either," said a senior White House official before Reagan departed on a nine-day European trip centered around the 13th economic summit here of the seven industrialized democracies. His reference was to Reagan's 1984 campaign slogan, "It's morning again in America."

While the official acknowledged that Reagan had been damaged by a series of events, especially the Iran-contra scandal and the loss of the Senate to the Democrats last year, he contended that the president could still seize the initiative on arms control and other issues during the final 18 months of his term.

But some officials say privately that they are doubtful that Reagan can do more than simply survive. They are worried that the 76-year-old president may be slowing down and that the economy may be cooling off after a long period of prosperity.

"There's no juice anymore," said an official here today, reflecting on the lack of administration initiatives on a trip expected to be the last European visit of the Reagan presidency.

Even the usually optimistic president has made few claims for what is shaping up as a summit of low expectations.

In speeches and conversations with allied leaders, Reagan plans to speak out on subjects including AIDS and economic freedom. White House officials said he will give particular emphasis to arms control negotiations with the Soviet Union and to allied military cooperation to protect the flow of oil supplies through the Persian Gulf.

But even before Reagan gave his first speech of the trip -- a 20-minute discourse on summit themes that will be televised in Western Europe on Friday morning -- officials were cautioning reporters to expect little in genuine results.

Reagan is bringing no new economic proposals. He had planned to celebrate the 40th anniversary of the Marshall Plan that rebuilt Europe with a speech in the historic Roman building where the European Community was born, but the speech and Reagan's state visit were scrapped after the Italian government collapsed.

White House officials privately admit it is unlikely that either Britain, where elections will be held Thursday, or France will join in a cooperative effort to escort oil tankers through the Persian Gulf. West Germany and Japan are prohibited from undertaking military roles by restrictions in their constitutions.

Both France and Britain now provide naval escorts for their own ships through the gulf. Reagan has accepted a plan from the Joint Chiefs of Staff to beef up U.S. naval forces in the region and to use them to escort American-registered Kuwaiti tankers through the gulf.

After years of urging the allies not to sell arms to Iran -- a project known as Operation Staunch -- administration officials are on the defensive here because of the Iran arms deal.

The highest White House hopes, both on the present trip and in the remainder of the Reagan presidency, are pinned on progress in arms control negotiations with the Soviet Union.

A Washington Post-ABC Poll completed Monday shows that 62 percent of Americans approve of Reagan's handling of relations with the Soviet Union and that 67 percent believe he is serious about making progress on arms control issues. These ratings are far higher than Reagan receives on his overall handling of foreign policy.

National security adviser Frank C. Carlucci said on Air Force One en route from Washington that the administration expected the summit participants to issue a statement expressing a common position on an agreement with the Soviet Union to eliminate medium-range nuclear missiles in Europe.

Today, White House spokesman Marlin Fitzwater opened his daily briefing by reading a statement by Reagan welcoming West German support for the early elimination of these missiles and calling NATO actions on this issue "a major success story" that lays the foundation for an arms agreement. Fitzwater said it moves the superpowers a little closer to a new summit meeting.

The White House also hopes to win favorable news media attention for Reagan at a speech he will give in Berlin at the Brandenburg Gate on June 12 that will stress his support for freedom and the peaceful reunification of the two German states.

Reagan also hopes to make a positive impact by meeting at the Vatican Saturday with Pope John Paul II on the eve of the pontiff's weeklong trip to Poland. It will be the third meeting between them.

On his first trip to Europe as president in 1982, Reagan nodded off briefly during a televised appearance with the pope. Aides blamed this embarrassment on a grueling schedule in which Reagan flew to Rome the morning after a long concluding day of the economic summit, which that year was held in Versailles, France.

This year Reagan should be well-rested after two full days of relaxation at a 17th-century villa 11 miles north of Venice during which his most strenuous official activity will be the taping of two speeches.

"We're not taking any chances this time," a White House official said.