Britain and Ireland resumed their efforts to close a deal on restoring home rule in Northern Ireland on Tuesday with expressions of optimism but no immediate signs of a breakthrough. A high-profile summit in England last week failed to produce agreement on a new peace settlement for the province, despite London and Dublin saying they were close to securing the end of the Irish Republican Army (IRA) as an active guerrilla group. "There's no reason why the remaining issues can't be sorted out very quickly -- within the week," said a British source as ministers opened a fresh round of negotiations in Belfast. Last week's talks at Leeds Castle, southeast of London, had been billed as a last chance to salvage the 1998 Good Friday Agreement, a peace deal which set up home rule institutions to share power between divided Protestant and Catholic communities. The U.S.-brokered pact has largely ended three decades of conflict which claimed 3,600 lives, but failed to heal deep sectarian divisions or provide stable government in the British-ruled province of 1.7 million people. --MORE 2317 Local Time 2017 GMT