Canada: thumbs up to free trade. Prime Minister Brian Mulroney won big on Monday. The Conservative Party victory - broad-based and larger than many expected - is likely to bring swift passage of the historic free-trade agreement between Canada and the United States.

``A leap of faith.'' That is how Canadians are describing their decision Monday to return to office with a solid majority the Progressive Conservative government of Prime Minister Brian Mulroney. The election results ensure passage in Parliament of a free-trade arrangement with the United States.

The quotation is from a royal commission that recommended such a deal three years ago. The words reflect the fear many Canadians have of closer economic ties with their powerful southern neighbor.

Twice in the past century Canadians have rejected free trade. Many governments have had programs to diversify Canadian trade away from the US. Yet inexorably, the proportion of trade with the US has marched upward over recent decades.

Now Canadians have decided consciously to encourage ``continentalism'' - to remove tariffs and many other barriers to commerce with the US. This comes despite a campaign by both opposition parties which depicted free trade as damaging if not devastating to Canadian independence, culture, regional development programs, and social systems.

``This country has rejected a hysterical appeal to narrow nationalism,'' said Bruce Phillips, Mr. Mulroney's communications director. ``In the main it has refused to believe the characterization of the trade agreement that [Liberal leader John] Turner made the cornerpiece of his campaign.''

Mr. Turner, in his concession speech, noted that a majority of Canadians voted for his party and the other opposition party, the left-of-center New Democratic Party (NDP). Thereby, he said, they ``expressed their wish to keep this country strong, sovereign, and independent.''

The Tories won 43 percent of the popular vote.

In the parliamentary system, however, the party with the largest number of votes in each constituency wins the seat. Because the opposition votes were split, the Conservatives were able to win 169 seats, well above the 148 needed for a majority.

The Liberals doubled their seats to 82. But they were expected to make major gains after the ``fluke'' Tory sweep in the last national elections in 1984. Two weeks ago, after Turner did well in nationally televised debates, the Liberals were briefly at the top of at least one public opinion poll.

The NDP ended up with 44 seats, their highest ever in the House of Commons. But their popular vote reached only about 18 percent, their traditional level. Party Leader Ed Broadbent confessed his disappointment. Early in the seven-week campaign the NDP had hopes of replacing the Liberals as the official opposition party - the No. 2 slot in the House.

Mulroney is expected to call Parliament into session as soon as possible, perhaps Dec. 12, and request swift passage of the legislation carry out the trade deal he signed Jan. 2 with President Ronald Reagan.

Turner, who asked that the Liberal majority in the nonelected Senate hold up the free-trade bill until the Canadian people had a chance to vote on the issue, is expected to remove that block as promised. This would mean the free-trade agreement would take effect Jan. 1. Some tariffs and nontariff barriers to trade will disappear immediately. Others will decline gradually over as long as 10 years to allow industry on both sides of the border to adjust to the increased competition.

Prime Minister Mulroney praised the opposition for their ``hard-fought campaign,'' adding, ``We are all Canadians and all love our country, Canada.''

Other implications of this election:

The Tories will be represented in the House in all provinces except tiny Prince Edward Island, whose four seats went to the Liberals; this is seen as useful for national unity. In the Liberal governments preceding that of Mulroney, the Liberals had no seats in most of the West, a fact that encouraged feelings of separation from Ottawa in that region.

The Tories won 63 of 75 seats in Quebec, maintaining their hold on a province that had for many decades before 1984 been a stronghold for the Liberals.

Moreover, the Tories snatched 48 of 99 seats in populous Ontario. This was better than expected since Ontario has been seen as the heart of the anti-free-trade vote.

The Tory victory will please the emerging Bush administration in Washington. James Baker III, designated as secretary of state, was the man who stepped into the free-trade negotiations in the fall of 1987 when they appeared destined for failure and whipped together a deal with his Canadian counterparts.

One touchy issue, however, could be acid rain. Most Canadian observers expect President-elect Bush to be somewhat more accommodative in this regard than President Reagan.

Approval of free trade is expected to give a boost to the current worldwide trade negotiations under the General Agreement on Tariffs and Trade. A mid-term review of progress under this ``Uruguay round'' will take place in Montreal starting Dec. 5.

In such negotiations, each nation usually negotiates reductions in trade barriers first with its chief trading partner. Agreed on concessions must then be granted all participating nations. Since Canada already had a trade deal with the US, it is expected to concentrate its efforts on seeking concessions from others, including the European Community and Japan.