A Montreal corporate president, Brian Mulroney, captured the leadership of Canada's major opposition Progressive Conservative Party tonight in a narrow victory over former prime minister Joe Clark.

Mulroney, 44, who has never held elected office, won by amassing 1,584 votes to Clark's 1,325 in the fourth round of voting by about 2,900 delegates representing electoral districts across the country at a four-day party convention. In percentage terms, the victory was 54.5 to 45.5 percent.

A champion of free enterprise, Mulroney is considered on the right side of the broad spectrum of conservative political thought encompassed by the Tory party in Canada. On foreign policy, he has expressed the most pro-U.S. views of any of the eight candidates who competed for the Conservatives' stewardship, calling for an intensive effort to improve investment and trade ties with the United States and defending President Reagan's actions in Central America.

Although a national election is not expected for about a year, the Conservative Party is currently far ahead of Prime Minister Pierre Elliott Trudeau's Liberal Party in public popularity, as measured by opinion polls. Most observers think the conservatives have a good chance of taking power here in the 1980s.

Mulroney is the first Quebecker ever chosen to head the national Tory party which traditionally has been strong among English-speaking Canadians, particularly in the western provinces.

His election opens the possibility of new bride-building between Canada's French and English cultures, whose differences have been a constant sourcre of internal friction.

In accepting victory, Mulroney said that the long and gruelling balloting was "a triumph of democracy," and, in an attempt to heal the party's internal bickering, he praised Clark for having led the party with "dignity, honor and courage."

The succession of dramatic ballots lasting about nine hours reflected the deep splits within the party over the leadership. Clark was out in front in earlier ballots, but Mulroney gradually gained strength as lesser candidates dropped out, freeing their supporters among the delegates to vote for other candidates.

A decisive moment came after the third ballot, when Member of Parliament John Crosbie was forced off the slate.

A large number of Crosbie's supporters, who numbered 858 on the third ballot, chose to back Mulroney in the last round of voting.

Clark, also 44, was plagued by a so-called ABC--"Anybody But Clark" campaign. As leader of the Tories, he has never been able to overcome widespread dissension within the ranks of his own caucus of members of parliament. He has been attacked by fellow Conservatives for allegedly lacking the charisma to be an effective national vote-getter for the party.

There is also deep resentment over Clark's handling of his short-lived administration in 1979. The first leader of a Tory government in Canada in more than a decade, Clark was toppled by the Liberals in a vote of confidence in the House of Commons after only nine months.

After enduring years of backbiting from within his party, Clark called a leadership campaign at a party convention in January when a large bloc of delegates voted against his continued stewardship.

Another problem for Clark has come from rightist elements of the party. These Tories, whose ranks included leadership candidate Peter Pocklington, owner of the Edmonton Oilers hockey team, espoused policies in many ways similar to those of President Reagan.

Among the right wing, Clark's moderate positions on maintaining social-welfare spending at close to current levels and compromising with the often-fractious French Canadians in Quebec were unacceptable.

Mulroney has been president of the Montreal-based Iron Ore Coil. of Canada. He speaks fluent French as well as English and based his campaign on votes from the Conservatives in Quebec. After losing to Clark in the 1976 leadership contest, he declined to seek a seat as a member of Parliament.

Born into a poor family in a small Quebec town, Mulroney became a labor lawyer and made his mark publicly investigating corruption in a government inquiry into the construction industry in Quebec.