Canada and the United States have agreed to substantial cuts in import duties on a wide variety of commodities, a move that will lead toward major integration of their economics, U.S. officials said today.

The agreement was reached in talk between Vice President Mondale and senior Canadian officals and was part of a series of bialateral understandings designed to stimulate the economics of the two countries and provide for more efficient use of their resources markets.

Modale arrived this morning in Tiyas capital of Alberta Province, which is rich in oil and natural gas. He hailed the outcome of his talks yesterday with Prime Minister Pierre Trudeau in Ottawa as reflecting a "new commitment to work together as equal partners to solve the problems which challenged a shared future on this continent."

Apparently the United States has agreed to puch for big tariff cuts on a number of commodities that are of vital interest to Canada in the multilateral trade talks that will reconvene in Geneva next week.

Although the agreement revealed today is in part bilateral, the tariff cuts will be negotiated as part of the broad multinational talks.

U.S. sources said that Canada will announce within a few days its willingness to join the United States, Japan and, apparently, the European Economic Community, in pushing for an ambitious reduction of tariffs averaging 40 per cent.

But Canada's decision to join the major Western powers came after the United States agreed to puch for tariffs cuts bigger than the 40 per cent formula on a number of commodities of vital interest to Canada.

During the Kennedy Round of trade talks in the 1960s, Canada took advantage of the tariff reductions negotiated among Japan, the Europeans and the United States without joining in the broad tariff-cutting itself.

Because of so-called most favored-nation clauses, Canada was the beneficiary of tariff concessions among the other major powers. These clauses require a country to give a tariff concession granted to one country to all other countries with which it has a most-favored-nation agreement.

The United States has been adamant that Canada will not get a similar free ride in the current round of tariff talks.

The new U.S.-Canadian effort at co-operation stands in contrast to the tension that marked bilateral relations during the Nixon-Ford years.

Annual trade across the border is in excess of $50 billion. Canada sells to the United States goods worth about $25 billion, roughly two-thirds of total Canadian exports.

U.S. exports to Canada amount to one-fifth of total U.S. sales abroad, equal to all sales in Western Europe or 2 1/2 times as much as annual exports to Japan.

Both American and Canadian officials attributed the warmer trend to the Carter's administration's interest in specific Canadian problems.

But Canada's preoccupation with its serious domestic problems also has contributed to Trudeau's decision to move away from the policy of the "third option," the term he applied in the past to lessening of Canada's dependence on U.S. markets by fostering other outlets.

The slump in the Canadian economy - the unemployment rate currently stands at 8.5 per cent while inflation is above 9 per cent annually - and the seccessionist movement in French-speaking Quebec have tended to dilute the nationist preoccupation to Canadians.

American investments in Canada, long a prime target for nationists decrying "foreign domination." appear to be welcome again in the new climate.

In Ottawa, the two sides agreed that in addition to taking anti-protectionist measures, they should work on arrangements to promote specialization, avoid duplication of production and create a larger market for each other's products.

American officials said that in this way both sides expected to stimulate bilateral trade create additional jobs, and reduce consumer prices. Hence the American side was expected to lower tariffs on such items of special interest to Canada as petrochemicals, processed minerals and specialized industrial products.

Mondale said yesterday that Treasury Secretary Michael Blumenthal and the chief of the Council of Economic Advisers, Charles Schultze would meet with their Canadian counterparts in March to discuss issues in greater detail.

Today, Mondale said that Agriculture Secretary Bob Bergland also will come to discuss agricultural export problems.

Mondale and his party flew here to convince provincial government officials, including Premier Peter Lougheed, to sell more natural gas to the United States.

Alberta's 1977 fuel production is valued at more than $8.3 billion, or a 23.5 per cent gain over 1976. The province is now producing an additional 700 billion cubic feet of natural gas, which American industry hopes to buy since the Canadian government lifted its seven-year-old embargo on additional gas sales yesterday.

Lougheed is known to be interested in tariff cuts for agricultural products that the province exports to the United States.