VENICE, JUNE 7 -- Concerned by rapid shifts in U.S. foreign policy goals and methods in recent months, European leaders are likely to use the seven-nation summit here to press President Reagan to show more caution and consistency in world affairs.

The summit, which begins Monday night, could end up being a "damage control" mission by European leaders who see Washington's recent handling of Soviet-U.S. relations and events in the Persian Gulf as erratic and risky, aides to several of the key European participants suggest.

The growing likelihood of a new meeting between Reagan and Soviet leader Mikhail Gorbachev will contribute to political issues dominating the private dinner for the leaders that formally begins the Venice gathering, according to these aides.

The dinner will provide the leaders with an opportunity to seek an informal joint assessment of Gorbachev and the changes he is bringing to Soviet foreign and domestic policies, one of the leaders who will be at the dinner has suggested to aides.

While Reagan will be pressing the leaders of Britain, Canada, France, Italy, Japan and West Germany at this summit for an endorsement of his tentative agreement with Gorbachev to remove medium and shorter-range missiles from Europe, they will be asking him for clearer definitions of what the agreement will lead to, and what they could expect from a U.S.-Soviet summit later this year.

Reagan's unexpected near-agreement with Gorbachev at their meeting in Reykjavik, Iceland, last October to eliminate all nuclear-armed ballistic missiles, including the ocean-spanning variety, unsettled European leaders accustomed to a steady stream of anti-Soviet rhetoric and a strong buildup of America's nuclear arsenal under Reagan. The prospect of a sudden end to a 40-year-old policy of nuclear deterrence also stunned Europeans and many American strategists.

Reykjavik ended without any agreements being struck, but Gorbachev surprised Washington in February by agreeing to accept the elimination of medium-range missiles in Europe. The Reagan administration then had to push hard to obtain European acceptance of such a deal.

Reagan inadvertently revived concern about his commitment to the Western Alliance's standard deterrence policies on Friday in a speech that was televised in Europe.

He suggested that he is as opposed to nuclear weapons as the hundreds of thousands of Europeans who marched against the deployment of U.S. Pershing II and ground-launched cruise missiles in 1983.

"How I wanted to let them know that my heart was with them, that I too yearned for a day when mankind could live free of the terror of nuclear annihilation," Reagan said.

The largest marches were staged against the governments of British Prime Minister Margaret Thatcher and West German Chancellor Helmut Kohl, who will be attending this summit, as will French President Francois Mitterrand, whose support for deployment was vital to Kohl in overcoming the West German protests.

Thatcher, who will spend less than 24 hours at the three-day summit, will be meeting with Reagan for the first time since she held extended conversations with Gorbachev in Moscow at the end of March. She returns to London on Tuesday to resume campaigning for Thursday's parliamentary elections.

Having agreed to put aside their reservations about the "double-zero" option for eliminating U.S. and Soviet land-based nuclear missiles in Europe with a range of more than 300 miles, Kohl, Mitterrand and Thatcher will want to hear from Reagan about U.S. plans for dealing with the remaining Soviet superiority in conventional forces in Europe.

Japan's Prime Minister Yasuhiro Nakasone also has a strong direct interest in the medium-range accord, which would maintain the Soviets' right to station 100 such missiles in Asia while eliminating them in Europe.

The Europeans and Nakasone are also certain to use the summit to try to cool the increasingly belligerent exchanges between Iran and the United States over the Persian Gulf.

Here again, the swiftness with which Reagan has replaced one policy with its opposite has raised questions in the minds of policy makers abroad about the quality and character of the analysis on which the president is making foreign policy decisions.

After attempting to influence moderates in Tehran with arms shipments and then defending that decision as recently as March by saying that Iran had stopped terrorist actions, Reagan is now regularly denouncing Iran in the kind of terms that he used about Libya before an American air strike was staged against it in April 1986.

An administration campaign to call attention to threatening Iranian statements and actions has increased concern in European capitals that Washington might welcome a chance to shift attention away from Reagan's domestic troubles with an air strike against targets in southern Iran.

France has quietly begun to tell its citizens to leave Iran unless their presence there is essential. The warnings are said to have been related to a sweeping roundup by French police last week of Iranian-supported terrorist groups.

But informed sources say that concern over mob reaction against westerners if American raids were staged against Iran was also taken into account in the decision to pass quiet advisories to French businesses working in Iran.

Both France and Britain come to the summit prepared not to take up U.S. requests to increase their military presence in the gulf, according to diplomatic sources in both nations. Both turned down requests from Kuwait to get more directly involved in protecting civilian shipping in the gulf, while the Reagan administration ultimately agreed to do so.

France has rebuffed Washington on this request, while Thatcher has only said that she would consider it. Any renewed effort by Reagan to get greater French and British involvement would succeed only if he is able to convey a better sense of where such actions are likely to lead, allied diplomats say.