Fresh talks started last week in a bid to see the power-sharing government in the region resurrected.
The Stormont administration has been collapsed for more than two years following a breakdown in relations between the DUP and Sinn Fein.
Six previous talks initiatives to restore devolution have failed to find consensus.
The latest talks come shortly after an impassioned plea from a priest conducting the funeral service for murdered journalist Lyra McKee.
Father Martin Magill urged politicians present at the funeral at St Anne’s Cathedral in Belfast last month to work to restore Stormont.
Ms McKee was killed by the dissident republican group the New IRA during disturbances in Londonderry.
The local leaders of the Catholic Church, Presbyterians, Church of Ireland and Methodists were among the group which met Northern Ireland Secretary Karen Bradley, Irish deputy premier Simon Coveney and the political parties at Stormont House on Tuesday.
In a joint statement, they expressed hope that the new talks were a “fresh window of opportunity, born of tragedy”, but warned “courageous and compassionate leadership” is needed.
“As leaders of Ireland’s main churches, we want to add our collective voice to support and encourage everyone taking part in this new round of political talks to seize the opportunity for a new beginning that lies before them,” the church leaders…
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