BELFAST, Northern Ireland (AP) _ British and Irish troops, with spotter helicopters flying overhead, combed the Irish border Monday for IRA guerrillas who have killed 10 police officers and a soldier in four days.

Protestant politicians demanded a ''relentless offensive'' against the IRA, which is trying to drive the British from Northern Ireland and is outlawed on both sides of the border.

Officials gave few details of the operation along 80 miles of the frontier from Newry, where an Irish Republican Army mortar attack killed nine police officers Thursday, to Country Fermanagh, where IRA gunmen shot a police sergeant to death Sunday outside a Roman Catholic church.

''It's a major operation, and we're coordinating our efforts with the Irish army and police on their side of the border,'' said a British army spokesman who spoke on condition of anonymity.

Police sources in the Irish Republic said security units raided isolated farmhouses and other suspected guerrilla hideouts. No arrests were reported.

As the troops fanned out through the Sterrin Mountains along the zig- zagging border, the Royal Ulster Constabulary, Northern Ireland's police force, buried the last three victims of the Newry attack, which has plunged the province into yet another political crisis.

Echoing appeals for peace already made by Protestant clergymen at weekend burials, Roman Catholic churchmen pleaded Monday that the killing be stopped. In 15 years of sectarian bloodshed, at least 4,420 men, women children have been slain.

The bishop of Down and Connor, the Most Rev. Cahal Daly, said at the funeral of police reservist Denis Price in the Belfast suburb of Glengormley: ''No cause can justify murder.''

At the funeral of another reservist, Paul McFerran, 33, in nearby Carrickfergus, the Rev. Brendan McGarry, a Catholic priest, declared, ''This campaign of killing must stop.''

He urged Catholic politicians, ''If you have any influence over those engaged in this campaign, do anything in your power to persuade them that this is not God's way.''

In the Northern Ireland Assembly, the militant Protestant leader, the Rev. Ian Paisley, demanded that the British government ''embark upon a relentless offensive'' against the gunmen ''until the IRA and all terrorism are wholly erradicated.''

''The struggle with the IRA is a matter of life and death,'' Paisley declared at an emergency session of the advisory assembly.

The IRA is trying through its guerrilla war to wrest this Protestant- dominate d province from Britain and unite it with the predominantly Catholic Irish Republic.

Nineteen people have been killed in the province since Feb. 17, one of the bloodiest periods in Northern Ireland in years.

Paisley accused London of cutting back on security in Ulster, which he said ''led to the killings we saw in Newry.'' British army strength in Northern Ireland has been halved in recent years to 8,500 regulars as police are given a bigger share of security duties.

''The government has failed in its responsibility to protect this province,'' Paisley said. ''It has forfeited the right to govern. We don't want to hear words from the government. We want to see action.''

For the moment at least, the killings have doused fragile hopes of talks between Protestant and Catholic politicians to work out a settlement of political, religious and economic conflicts that have permeated the province's history.

Protestant extremists, generally dormant in recent years, have threatened to retaliate against the overwhelmingly Catholic IRA and its supporters, including those hiding in the Republic.

The moderate Belfast Telegraph said in an editorial Monday: ''Politics alone cannot stop those people who lob mortar bombs into police canteens or who kill on church doorsteps.

''The quest for political agreement will continue, but given the bleak outlook at present and the high level of violence in recent weeks, the priority must be to step up direct action against the gunmen and bombers.''