DUBLIN (Reuters) - The Irish government has called on Sinn Fein to help ensure the Irish Republican Army is put "firmly out of business" after police in Northern Ireland said the party's former military wing might have been involved in a recent murder.

An end to violence by IRA guerrillas was a central plank of a 1998 peace deal in the British province of Northern Ireland that put Sinn Fein into a power-sharing government with pro-British unionists.

The main unionist party last week threatened to bring down the power-sharing government after police said current or former members of the IRA may have been involved in the shooting dead of a former member earlier this month.

If it leaves, the governance of Northern Ireland would revert to London in what would be a major setback for the peace process.

Irish Foreign Minister Charlie Flanagan said on Sunday a solution to the impasse required that Sinn Fein ensure its supporters cooperate with police, rebuild trust and make sure remaining IRA structures are dismantled.

"I believe that normal politics will only be introduced on this island fully if Sinn Fein uses its influence and its exhortations to ensure that the IRA is put firmly out of business," Flanagan told Irish state broadcaster RTE.

The Northern Ireland executive "will only be preserved if all the party leaders, and Sinn Fein in particular, work towards ensuring a level of trust and confidence that appears to be disappearing," he said.

Senior members of Sinn Fein, including politicians who were once members of the IRA, have denied the group still exists and said any ex-members involved with the murder must be prosecuted.

The Irish government is a co-guarantor of the 1998 peace deal that largely ended three decades of conflict between mostly Catholic nationalists, who favored unification with the Republic of Ireland, and Protestant unionists wanting to stay in the United Kingdom.

Sinn Fein members have accused the Irish government of using the crisis to damage Sinn Fein ahead of elections in the Republic of Ireland due next spring, a charge it has denied.

Flanagan said he would hold talks with Britain's secretary of state for Northern Ireland, Theresa Villiers, in the coming days and called for talks between all parties to break the impasse.

(Reporting by Conor Humphries; Editing by Mark Heinrich)