BELFAST (Reuters) - A breakaway Irish republican group said on Tuesday it had shot dead a policeman in Northern Ireland, the second such attack in two days on a power-sharing deal that has brought peace to the British-ruled province.

As long as there is British involvement in Ireland, these attacks will continue, the Continuity IRA, a small paramilitary splinter group, said in a statement carried by British media.

Politicians from all sides said the violence would not derail a process that has brought relative calm and increasing prosperity to Northern Ireland after 30 years of bloodshed between pro-British Protestants and Irish Republican Roman Catholics.

The policeman, named as Stephen Carroll, 48, was shot on Monday night while answering a call to a broken window in the town of Craigavon, 25 miles southwest of the province's capital Belfast, police said.

On Saturday, two British soldiers were shot dead in an attack claimed by another republican splinter group, the Real IRA, whose name is styled on the Irish Republican Army (IRA).

The IRA fought British rule for decades and drew support from the Roman Catholic community. But, along with pro-British Protestant guerrilla groups, it agreed to cease hostilities under the Good Friday peace deal in 1998.

By then, sectarian violence had killed more than 3,600 people in Northern Ireland in some 30 years of Troubles.

British Prime Minister Gordon Brown said the latest wave of violence would not disrupt the peace process.

These are murderers who are trying to distort and disrupt and destroy a political process that is working for the people of Northern Ireland, Brown said. They will never be allowed to undermine the historic political process.

GROUPS HAVE 'STRONG LINKS'

The Continuity IRA probably has 50 to 80 members, mainly based over the border in the Irish Republic, said Carina O'Reilly, European analyst for Jane's Information Group.

The dissident group, which wants a united Ireland, has made recent efforts to recruit and, while it probably has strong links to the Real IRA, has a more radical ideology, she added.

She said both the Continuity IRA and Real IRA had the weapons and sophistication to sustain the activities of the last few days.

Northern Ireland police chief Hugh Orde told a news conference: We will pursue those responsible ... to the ends of the earth ... We will solve these crimes, we will deliver justice and we will allow the peace process to continue.

He ruled out asking the army for help in tackling what he described as a small, disenfranchised and rather ridiculous group, saying: It is not necessary and it doesn't work.

Northern Ireland First Minister Peter Robinson said there was a battle of wills between the political class and the evil gunmen, adding: The political class will win.

Deputy First Minister Martin McGuinness, a senior IRA commander in the 1970s, described the killers as traitors to the island of Ireland.

They have betrayed the political desires, hopes and aspirations of all the people who live on this island, he said.

During the Troubles, Republicans viewed the province's police force, known then as the Royal Ulster Constabulary (RUC), as a partisan extension of British political rule that sided with the Protestants. More than 300 RUC officers were killed.

The RUC was disbanded and relaunched as the Police Service of Northern Ireland in 2001 in an attempt to provide a more impartial force with support from Protestants and Catholics.

(Additional reporting by Carmel Crimmins, Jonathan Saul and Michael Holden; Writing by Peter Griffiths; Editing by Kevin Liffey)

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