Britain proposed today that Northern Ireland be governed by a locally elected legislature and executive that would give the Catholic minority a significant share of power in the British-ruled province. c

The power-sharing proposals, which will be discussed with political leaders of the Catholics and the Protestants, who make up two-thirds of Ulster's population, constitute a major initiative by Prime Minister Margaret Thatcher to seek a peaceful solution of the sectarian strife there.

The proposals came in a government white paper after weeks of intensive deliberations by Thatcher and key members of her Cabinet and months of preliminary consultations with Ulster politicians. Thatcher's goal is to present a workable Ulster home-rule plan to the British parliament this autumn and hold elections in Northern Ireland next year.

Although both Protestant and Catholic politicians in Ulster expressed initial skeptism today about the chances of success, Thatcher's secretary for the province, Humphrey Atkins, insisted at a press conference that "there are grounds for some level of optimism. I detect in my consultations that leaders of the political parties in Northern Ireland really want to find some way forward."

Thatcher's initiative is the latest in a long series of attempts to solve one of Europe's most intractable problems, an essentially tribal antagonism with roots in the 17th century. Protestant English and Scottish planters sent to colonize northeastern Ireland in the early 1600s remain to this day a breed apart from the Irish Catholics on the rest of the island.

When Ireland became independent in 1920, Britain kept the six northeastern counties when Protestants loyal to the British crown were in the majority. The grievances of the Catholic minority over job and other discrimination under the Protestant provincial government at Stormont Castle in Belfast erupted in the late 1960s in mass marches and violent clashes with Protestant paramilitary groups.

Britain sent troops in 1969. More than a decade later, after more than 2,000 deaths, the troops remain.

The crucial issues are Northern Ireland's relationship with Britain and the role its Catholic minority should play in running the province. Catholic leaders there want it united with the neighboring, predominantly Catholic, Republic of Ireland. Protestant leaders want Ulster to remain part of Britain and be run strictly by majority rule.

The white paper reiterates the British government's pledge that Ulster will remain part of Britain so long as a majority there wants it that way. But it proposes a much more substantial role for Catholics than they would have as the permanent minority in a strict majority-rule government whose cabinet was drawn only from the majority part or coalition.

The proposed legislature of about 80 members would be elected by proportional representation, virtually guaranteeing Catholics a third of the seats.

Under one alternative, members of the executive or cabinet would also be chosen by proportional representation by the legislature or directly by the voters, also guaranteeing Catholics some cabinet seats and authority over some government departments.

A more complicated alternative would set up a council -- half from the majority, half from the minority in the legislature -- with the power to delay, refer back or block actions taken by the legislature or a majority-party cabinet.

Atkins said earlier alternative would "make sure the minority has some authority, some influence over what the government does. It would create a very considerable role of the minority.

He also acknowledged that Uslter Protestant political leaders remain publicly opposed to such power-sharing and that dissident Protestants were able to wreck a similar plan in 1973. But Atkins added that he believes both Protestants and Catholics are now eager to end a decade of direct rule of Ulster from London and will try to find points of agreement in separate, private negotiations with him.

The British proposals would return most of the self-government power taken away when Britain abolished the Protestant-run Stormont government -- which had ruled for half a century -- at the height of sectarian violence in 1972. A new government would have power over most economic matters, education, health, housing and social services, while London would retain control and security, police, courts and the overall size of the Ulster budget.

The proposals, which offer the Catholic minority the possibility of a larger share of power than was expected from Thatcher's Conservative government, were worked out by a special Cabinet committee that included Atkins, Home Secretary William Whitelaw (who attempted to introduce power-sharing when he was Northern Ireland secretary in the early 1970s), Defence Secretary Francis Pym (another former Northern Ireland secretary who now commands about 12,000 troops in Ulster) and Foreign Secretary Lord Carrington (whose skill at forced compromise was demonstrated in the Rhodesian independence negotiations).

The foundation of their proposals is that the Protestant majority "should be confident that Northern Ireland cannot be separated from the rest of [Britain] without the consent of the majority of its people" and the Catholic minority "should accept and respect this fact." "In response," the Protestant majority "should ensure a positive role for the minority in arrangements for the government of Northern Ireland." Both communities should "recognize and develop the links that exist between Northern Ireland and the Republican of Ireland."

The white paper includes several striking appeals to both Protestant and Catholic leaders to accept a compromise as the only way to heal their divisions and restore stability and prosperity. The "will to work together must come from the people of Northern Ireland themselves," the white paper declared. "In asking themselves whether they are prepared to make that effort, they should weigh carefully all that is at stake."

Atkins said the continuing violence in Northern Ireland and its increasingly depressed economy underline the urgency of achieving a politcal solution. "It would totally isolate the terrorists," he said, "a prize worth gaining."

There has been a lull in large-scale bomb attacks this year, which might be attributable to the recent conviction of Brian Kennan, believed to have been the Provisional Irish Republican Army's chief of terrorist operations. He was sentenced to 18 years in prison for directing a 1975 IRA terror campaign of bombings and shootings in England that killed nine persons and injured 153.

Still, 42 people have been murdered by terrorists this year as IRA gunmen pick off members of the Ulster security and prison forces, particularly in towns near the Irish border.

Two Ulster Protestant members of the British Parliament, the Rev. Ian Paisley and Harold McCusker, greeted the Thatcher government's proposals today with complaints about security and the economy."The fundamental concern of my constituents," said McCusker, "is to stay alive and have a job."

The decline of the economy, based on dying industries such as shipbuilding, textiles and heavy engineering, has been exacerbated by the years of violence and more recently by a deepening British recession. Unemployment in Ulster is twice that of Britain and as high as 35 percent in prodominantly Catholic West Belfast.

Atkins recently froze all government spending in Northern Ireland for several weeks while money is reshuffled to help prop up what remains of such once-mighty industries as the Harland and Wolff shipbuilding firm in Belfast. It is to receive about $150 million in additional government subsidies to protect its remaining 7,000 jobs for at least another year.

Stressing the need to achieve peace and stability as the basis for economic reconstruction, Atkins said, "The present economic situation in the province is a telling reminder of how urgent that task is, and how desirable it is for the elected representatives of Northern Ireland to be directly involved in it."