President Reagan and six other heads of state today buried their differences on key economic issues in a communique that reaffirmed their nations' "interdependence," but broke no new ground in dealing with the critical worldwide problems of inflation and unemployment.

The communique said that the "primary challenge we addressed at this meeting was the need to revitalize the economies of the industrial world." This will require, the seven leaders added, tackling unemployment and inflation at the same time, using a "range of policy instruments."

The communique, issued tonight after a two-day summit at the nearby Chateau Montebello in Quebec and here in Ottawa labeled their meeting a success, and accepted French President Francois Mitterrand's invitation to meet in Paris again next year.

Treasury Secretary Donald Regan told reporters that in his opinion the Europeans, who had come to Ottawa with strong complaints about high U.S. interest rates, "will go home feeling very satisfied."

But many of them, especially the West Germans, indicated that they feel the summit was "stonewalled" by the United States. In general, the suggestion is that the Americans in their briefings deliberately glossed over some of the more tense exchanges among the leaders during the plenary sessions.

The United States and the Europeans each apparently compromised on one key issue the other side considered important. The United States succeeded in incorporating some language on East-West trade into the communique -- the first time such an issue was so addressed -- while Canada, France and Japan were able to focus attention on the need for more aid to poor Third World countries.

As expected, the communique finessed the interest rate question. The document acknowledged that interest rates are at "record levels," and should they stay that high for a long period, they would "threaten productive investment."

Then, conceding the American argument, the communique acknowledged that "low and stable monetary growth" is essential to control inflation, even if a side effect turns out to be high interest rates "where fears of inflation remain strong."

But the next sentence addressed European complaints by saying: "We are fully aware that levels and movements of interest rates in one country can make stabilization efforts more difficult in other countries." In addition, the communique called for restraint of governmental spending to hold down deficits.

Still, there was no suggestion in the communique that the United States should alter its policy, although a new consultative process between summits is to be put into effect. Regan told reporters that after listening to the European arguments, "We will probably consult more with our partners. I don't think we've consulted as much as we should have."

American officials said they believed President Reagan had given "a strong" performance at the summit.

Tonight, Reagan joined the other leaders at a final press conference, expressing gratitude for "their degree of understanding and support for the economic policies we are embarked upon in the United States."

But while Reagan looked on impassively, West German Chancellor Helmut Schmidt and Mitterrand continued their barrage of complaints on interest rates. Schmidt said that "when I go back to Bonn, my government will begin to take decisions concerning the fact that unfortunately, for the time being, we will still have to deal with high interest rates."

As late as this morning, the Europeans were still trying to get language in the communique calling for intervention in foreign exchange markets to help stabilize foreign exchange rates. This pressure came largely from Mitterrand and Italian Prime Minister Giovanni Spadolini. The United States insisted that intervention would not serve to hold the dollar down in foreign exchange markets.

The Americans were successful in introducing language into the communique dealing with the perceived dangers of export controls so lax that the effect is to help the Soviet Union build its military strength. But the United States did not get everything it wanted although it was the first time that an East-West trade issue was addressed, even in generalities, in a Western economic summit communique.

Similarly, Canadian Prime Minister Pierre Trudeau, Mitterrand, and Japanese Prime Minister Zenko Suzuki were able to draw attention to the need for more aid to the poor countries of the Third World. But the language on this commitment was responsive to American fears, as one official put it "of going in blindly and losing our wallet."

On the East-West trade issue, the communique spoke of the need for improved consultation to make sure that the economic policies of the seven summit nations "continue to be compatible with our political and security objectives. We will undertake to consult to improve the present system of controls on trade in strategic goods and related technology with the U.S.S.R."

The United States was not successful in getting a reference in the communique to what it believes is the danger of increasing "vulnerability" of Western countries to Eastern resources and markets. There is particular concern over West German intentions to buy a substantial amount of natural gas from Siberia.

West German officials reportedly were bitter about the American focus of this issue, and scoffed at Secretary of State Alexander M. Haig Jr.'s suggestion that the United States could offer substitute energy for the Siberian gas.

On Third World aid, the communique said there was a need for "maintaining a substantial and growing" amount of official development assistance and spoke hopefully of prospects for a North-South summit to be held in Cancun, Mexico this fall. It also said there must be an awareness of growing poverty among the poorest of the poor nations.

But on Trudeau's effort to launch "global negotiations" to deal with Third World aid problems, the communique used deliberately qualified language. The leaders, the communique says, "are ready to participate in preparation for a process of global negotiations in mutually acceptable circumstances offering the prospect of meaningful progress." At President Reagan's insistence, the phrase "global negotiations" used a small letter g and a small letter n, rather than capital letters, as had been proposed by Trudeau. U.S. officials insisted this was a significant, symbolic change.

The United States fears that "global negotiations" on the scale Trudeau and the Third World favor could result in highly inflationary projects that would bypass the World Bank and International Monetary Fund, eventually resulting "in tampering with the world's wealth and redistributing it," as some officials put it.

At the same time, the summit leaders took a jab at "the Soviet Union and its partners" for making only "meager" contributions to Third World countries.

In terms of the much debated question of an "energy affiliate" for the World Bank, which had been endorsed at the Venice summit last year, the leaders this time merely suggested that they would cooperate with OPEC countries in helping to finance oil development in the Third World through the existing structure of the World Bank.

There was less difficulty in agreeing on trade issues, once it was determined that there would be no public ganging up on Japan. The communique reaffirmed the commitment to a "liberal" that the West Germans prefer, rather than the standard formulation, "free trade.")