President Reagan and French President Francois Mitterrand moved quickly tonight at the beginning of the seven-nation economic summit here to dispel fears that a major U.S.-French monetary conflict would disrupt harmony among the western allies.

"No one seems to have come here to pick a fight at all," said a senior U.S. official who briefed reporters on a 40-minute meeting between Mitterrand and Reagan, which was also attended by several of their top advisers.

To underscore their demonstration of amity, the two presidents used the occasion to announce that Mitterrand has accepted Reagan's invitation to visit the United States again next year.

That meeting and what was reported to be an equally harmonious half-hour conversation between Reagan and British Prime Minister Margaret Thatcher were the primary business of a day filled mostly with pageantry as Reagan greeted and hosted dinner for the arriving leaders of Britain, France, West Germany, Italy, Japan and Canada.

Reagan also proclaimed today in his weekly radio broadcast that the United States is leading the allies toward economic recovery, but he did not mention the opinion of many economists that high U.S. interest rates had helped lead these same nations into recession and could diminish the recovery.

"Since the last summit in France a year ago we've made important progress," the president said in his radio address. "Today America is leading the world into an economic recovery that's already being felt in many of the countries represented here."

U.S. officials had been concerned about Mitterrand's call in a recent speech in Paris for a new global monetary conference patterned after a 1944 meeting at Bretton Woods, N.H. Mitterrand, whose government has been troubled by a steep fall in the value of the French franc in relation to the dollar, proposed moving away from the present floating system of currency relationships to a more rigid system.

But a senior U.S. official said tonight after the Reagan-Mitterrand meeting that the French president "only feels it's time to start a process of fundamental thinking about the broad nature of the international economic system." He added that Mitterrand is not attempting to match the old Bretton Woods system itself "but to duplicate that act of imagination in looking at our problems."

A senior French official gave a similar account of the Reagan-Mitterrand meeting, suggesting that there will be a noncontroversial discussion of monetary matters at the seven nations' ninth economic summit here this weekend along the lines Mitterrand suggested. He said that the notion that France was insisting on a new Bretton Woods conference was "a misunderstanding that has been avoided."

Thatcher also stressed the need to demonstrate western unity in her meeting with Reagan, saying that she hopes the summit will send "a message of hope" about the world economy, according to a British official. Her view, the official said, is that "the world economy is moving."

Thatcher, who is taking time out from her re-election campaign in Britain to attend the first 24 hours of the summit meeting, met with Reagan in the garden of the brick and clapboard Providence Hall, where the president is staying here. She also met with Japanese Prime Minister Yasuhiro Nakasone and German Chancellor Helmut Kohl.

Officials said that Thatcher did mention to Reagan the British opposition to his administration's export administration bill, which would give U.S. law precedence over foreign law for subsidiaries of American countries operating abroad. Reagan was reported to have taken note of her opposition but did not indicate any change in his view.

Thatcher was also said to have "mentioned" large U.S. budget deficits in discussing economic policy. However, she did not make or imply criticism of the president, according to officials.

Her government has complained in the past that U.S. deficits are responsible for keeping interest rates high here and worldwide. Both Reagan and Thatcher were said to be cautiously optimistic about the prospects for economic recovery, as were Nakasone and Kohl in their talks with Thatcher.

On his flight from Bonn, Kohl also expressed "cautious optimism" about world economic recovery. He said the upbeat mood as the summit began was fortified by positive signs that the U.S. economy is primed for a strong upturn.

However, West German sources said that, even though Kohl and the other summit participants were eager to cooperate with the Reagan administration in making the summit a success, the Europeans would stress the dangers of high interest rates linked to U.S. budget deficits. But the West Germans said that such warnings would be couched in discreet, courteous language to avoid open conflict.

In addition to the extended talks with Thatcher and Mitterrand, Reagan had a 10-minute individual welcoming meeting with the each of the six leaders this afternoon at the brick Governor's Palace in a heavily secured section of Colonial Williamsburg that was closed to the public. The palace was the residence of the British colonial governor before the American revolution.

The seven leaders will hold their first formal summit session Sunday morning in seclusion at the historic Virginia House of Burgesses before joining their foreign and finance ministers in the afternoon at the Williamsburg Inn. The seven leaders will be spending much of their time together at meals and private meetings.

Reagan, who has been carefully briefed for days for his role as moderator, has said he wants to emphasize economic recovery. He also appeared today to be anxious to avoid impromptu controversy on other issues.

On one of the few occasions today when a reporter came within shouting distance of Reagan, she called out, "Mr. President, what about the Soviet missile threat?"

"All I can do is wave," Reagan replied.

The other national leaders who arrived today were Canadian Prime Minister Pierre Elliott Trudeau and Italian Prime Minister Amintore Fanfani. Gaston Thorn, president of the Commission of the European Communities, also is attending.

Thorn and the six national leaders arrived in a series of helicopter landings in Market Square where military bands and a bewigged, red-coated fife, drum and bugle corps played "Yankee Doodle" and the six countries' national anthems. The official delegations were then taken by horse-drawn carriage to confer with Reagan at the Governor's Palace.

The fife, drum and bugle corps substituted "The British Grenadier" for "Yankee Doodle" when welcoming Thatcher to avoid stirring Revolutionary War echoes. But not all went that well.

As Nakasone was being escorted to the Governor's Palace by Reagan, the Japanese contingent was startled to hear the band break into "The Battleship March," a World War II song used to raise the morale of Japanese navy crews going to battle that has since become a rarely played, but widely recognized symbol of militarism in Japan.

Trudeau was welcomed with "The Maple Leaf Forever," which stirs unpleasant memories in French Canada by celebrating the defeat of the French when Quebec fell to the English in 1759.

Reagan yesterday issued a three-paragraph statement replying to leaders of third-world nations who asked in a letter that the seven summit nations give attention to the problems of underdeveloped nations. Reagan's statement said that the summit participants would heed this request and were mindful of "the circumstances and concerns of the poorest nations who need our cooperation most."

In his radio address today, as in many recent statements, Reagan opposed protectionism and hailed the reduction of inflation in the United States.

"All of us seek the same goal: a healthy, sustained economic recovery that will revive troubled economies in North America, Europe and the rest of the world," Reagan said.