President Reagan arrived here tonight saying it was his "fervent hope" that he and Soviet leader Mikhail Gorbachev "can at least make a start" on resolving the deep differences between the two superpowers at their summit meeting, which opens here Tuesday.

The Soviet leader arrives here Monday morning for eight hours of talks Tuesday and Wednesday with Reagan in what will be the first summit meeting between U.S. and Soviet leaders in more than six years.

Complimenting the Swiss government for hosting the summit and for its commitment to freedom, Reagan said, "It is to make certain that this great work on behalf of human freedom can go forward in peace that I have come here today . . . . I am convinced American-Soviet relations need a fresh start, a genuine give-and-take on regional conflicts, on human rights, and on reduction of arms.

"American and Soviet differences on these matters run deep. Mr. Gorbachev and I cannot surmount them in only two days. But I'm here in the fervent hope that on behalf of all the people of the world, we can at least make a start."

The arrival of the president gave the United States a place on the international stage here that has been dominated by a large and relatively sophisticated Soviet public diplomacy operation, in place for much of this week.

In a press conference here today, a Soviet spokesman hinted that Gorbachev will be bringing new arms proposals when he arrives for the summit. "The general secretary has said he will not come with empty hands," the Kremlin spokesman said. "It will be interesting to see what he means."

Despite the momentum provided by last-minute breakthroughs in negotiations for an American-Soviet cultural agreement and other joint programs and the strong hint from Soviet officials that Gorbachev will arrive from Moscow with fresh arms control proposals, the two sides remain sharply divided on the key summit agenda topics of arms control and regional conflicts, according to Soviet and American officials here.

Local officials here consider their role as hosts to the summit the most ambitious international undertaking in this French-speaking Swiss city's history. The city has braced for the flood of visitors from East and West, including about 3,000 journalists, with stepped-up security.

Today, a demonstration by several thousand Swiss broke a mood of distant curiosity the city's residents have displayed. Chanting for "freedom," the demonstrators carried banners that posed a mixed bag of appeals to both the Soviet and American sides. They called for Soviet troops to get out of Afghanistan and for the United States to end its involvement in El Salvador, among other things.

Reagan, 74 and nearing the end of his political career, is poised to carry on the tradition begun 30 years ago when Dwight D. Eisenhower met here with Soviet Premier Nikolai Bulganin for the first postwar U.S.-Soviet summit. It is the 11th such meeting to take place between Soviet and American leaders since the end of World War II.

After his arrival at 10:30 tonight, Reagan rushed off to La Maison de Saussure, the 18th-century mansion north of Geneva where he and Mrs. Reagan will stay.

Gorbachev, 54, is scheduled to fly into Geneva's Cointrin airport Monday afternoon with his wife, Raisa, 53, and an entourage of close Kremlin advisers, according to Soviet officials. It is his second trip to the West since assuming power in March and his first meeting with a U.S. leader.

Tuesday morning, when Reagan and Gorbachev hold their first meeting at Fleur d'Eau, a small chateau on the shore of Lake Geneva, they will end a chapter in the post-detente era that began with the 1979 Soviet invasion of Afghanistan and has kept U.S. and Soviet leaders at arm's length.

Altogether, they have scheduled four sessions -- for a total of eight hours -- Tuesday and Wednesday. In addition, the Reagans and Gorbachevs will dine together both days.

Before departing Thursday, the two leaders plan to discuss four topics: arms control, regional issues, human rights and bilateral issues. They have agreed to conclude the two days of meetings with a joint appearance.

Reagan remains firmly committed to the Strategic Defense Initiative research program, which Gorbachev strongly opposes.

And, in a briefing here today, Soviet officials indicated no forthcoming movement in Moscow's entanglements in Afghanistan or four other areas of regional strife involving Soviet or Soviet-backed troops. Reagan has identified the regional conflicts as the key subjects to be discussed at the meetings.

Since the summit was announced in Washington and Moscow July 3 -- and particularly in the past few days -- both Reagan and Gorbachev have positioned themselves to reap full advantage from the meeting.

For Reagan, the summit crowns a political career that he has fashioned over decades as a hard-line critic of Soviet aggression abroad and abuses at home. The U.S. president views the summit as a chance to ease world tension over military conflicts in Afghanistan, Nicaragua, Ethiopia, Angola and Cambodia.

Each case, Reagan said in a speech at the United Nations last month, is the "consequence of an ideology imposed from without." And in each case, he added, "Marxism-Leninism's war with the people becomes war with their neighbors."

In the speech, he outlined a proposal for resolving the conflicts, which he is likely to raise during the talks.

It was Reagan who initiated the summit in an invitation that Vice President Bush delivered to Gorbachev when he attended the funeral of Gorbachev's predecessor, Konstantin Chernenko, in Moscow last March. Gorbachev quickly agreed to the idea in principle. After several months of haggling, the two sides set the place and time of the summit in a Washington meeting in July between the Soviet ambassador to the United States, Anatoliy Dobrynin, and Secretary of State George P. Shultz.

With only 250 days in the Kremlin behind him and a major congress of Soviet Communist Party officials scheduled for late February, Gorbachev has more to risk at the summit table than his American counterpart, according to western analysts.

"He has no record for dealing with someone like Reagan," said one senior diplomat in Moscow in an interview, "and the whole world is watching to see how he handles it."

In a speech to Soviet Nobel laureates in Moscow Wednesday night, Gorbachev reaffirmed his intention to use the summit to negotiate limitations on SDI.

Since then, his Kremlin aides have mounted a campaign to gain international support for the Soviet stance against SDI and use it to wedge Reagan away from his support of the controversial program.

In Geneva, senior Kremlin officials have conducted a series of briefings for international journalists to decry U.S. arms-control policies and defend Moscow's line on other topics on the summit agenda, including human rights and Afghanistan and other regional conflicts.

In recent days, the official press in Moscow has hardened its rhetoric against the Reagan administration by publicizing a series of alleged U.S. human rights violations and high-pitched criticism of what is portrayed as U.S. militarism.

In a well-publicized press conference Thursday, Vitaly Yurchenko, an alleged KGB officer who defected to the United States and then redefected to the Soviet Union, held a press conference to rail against his "harsh" treatment at the hands of the CIA, apparently to demonstrate U.S. human rights "violations."

The Soviet Union also stepped up moves yesterday to improve its image in the West in advance of the summit by granting 10 Soviet citizens permission to reunite with their families in the West.