Former prime minister James Callaghan resigned today as leader of Britain's opposition Labor Party, leaving his succession to a bitter power struggle between the party's deeply divided left and right wings.

Callaghan urged Labor members of Parliament to move quickly and follow tradition by electing a new leader before Parliament reconvenes next month.This selection process is believed to favor narrowly former chancellor of the exchequer Denis Healy, who would continue Callaghan's centrist leadership, including support for a mixed economy and British participation in NATO and the European Community.

On the other hand, the insurgent left wing of the party, led by former energy minister Tony Benn, has demanded that Labor deputies hold off or select the present deputy leader, Michael Foot, as a caretaker, until party activists decide at a special meeting in January on the composition of a new electoral college to select the leader.

They hope this process would produce a party leader who would be more receptive to the left's call for greatly increased government control of the economy, withdrawl from the Common Market and unilateral nuclear disarmament by Britain. The left succeeded in having these positions adopted as official policies at the party's stormy annual conference in Brighton earlier this month.

Healy and his supporters made clear today, however, that he will be a candidate for election as leader by the duputies in their traditional balloting, which will begin at the end of this month. They strongly hinted that, if he wins, he would not step down if someone else were later selected by the party's new electoral college next year.

This could leave Labor with both a parliamentary leader eligible to become prime minister when it next won control of Parliament and a separate leader of the party organization, as is the case in West Germany, where Chancellor Helmut Schmidit is the Social Democratic Party's parliamentary leader and former chancellor Willy Brandt is the party organization's leader.

This "two pops" prospect could so antagonize the left that the party would be torn apart. The left-wing activists' Campaign for Labor Democracy, which wants Benn elected leader, warned today that if the Labor deputies "insist on holding a full leadership election in defiance of the recent [party] conference decision, this will be regarded by many constituencies as a declaration of war."

On the other side, legislators from Labors's center and the right wing have warned that they might split from the party if the left tried to force an unacceptable leader on them.

Besides Healy, Foot and Benn, the other leading candidate to succeed Callaghan is Labor's spokesman for foreign affairs, Peter Shore, a lean, shy centrist who cautiously supports some policies advocated by both the left and right wings, including possible withdrawal from the European Community.

Healy, a burly, abrasive, sharpwitted in-fighter, claims most of his support from the right wing. Foot, a former journalist and gifted orator, is popular with Labor's union supporters, but at 67 is considered too old to do more than try to keep the party together until the power struggle is settled and a broadly acceptable leader is chosen.

Foot said tonight that it was "highly improbable" that he would be a candidate for the leadership.

The bitter battle for party control has tarnished Callaghan's departure from its leadership after 35 years in British politics, the majority of them in Cabinet or shadow cabinet positions. The caution and preference for delay and compromise that the former sailor had long used to steer through the shoals of power politics over the years has been blamed by the press and some Labor politicians for allowing the party to slide into chaos while Callaghan was making up his mind about retiring.

He told reporters today that he first considered stepping down after Labor was badly beaten by the Conservatives in the May 1979 national election and he was replaced as prime minister by Margaret Thatcher. "But every party has its problems after an election," he said, "and I wanted to give it a period of time and stand my corner."

Others in Labor's right wing have complained, however, that "Big Jim," a tall, imposing, patriarchal figure who remained the nation's personally most popular and respected politican, did not not use his prestige to stand up against the left-wing insurgents inside the party. The closest Callaghan came was an angry declaration at a meeting of the party's executive in Blackpool that he would not allow Tony Benn to be "foisted" on Labor deputies as their leader because "it would be a disaster" for the part at the polls.

Callaghan, 68, who said he will keep his seat in Parliament and speak out as an elder statesman on important issues, served as home secretary, chancellor of the Exchequer and foreign secretary in Labor governments between 1964 and 1976. He became party leader and prime minister in 1976 when Labor members of Parliament elected him to succeed Harold Wilson, who had suddenly resigned as prime minister.

He kept the minority Labor government in power another three years with skillfull parliamentary maneuvering, including alliances with Liberal, Ulster Unionist and Scottish and Welsh nationalist deputies that finally fell apart early in 1979. After Callaghan's government fell by one vote on a censure motion in Parliament, Labor lost in the resulting national election.

Critics of Callaghan's caution contend that he would still be prime minister if he had decided to call an election, as the country expected him to do, in the autumn of 1978, before a winter of widespread strikes that later cost the union-based Labor Party crucial swing votes.

As an international statesman, Callaghan maintained particularly close personal relations with President Carter and other Americans leaders. He also sent his son-in-law, journalist Peter Jay, to Washington as the British ambassador. Among his future interests are expected to be future interests are expected to be the health of the Atlantic Alliance and relations between the industrialized countries and those of the Third World.