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 said.
"In welcoming this fresh initiative, together, we hope and pray that there will be substantive progress over the next number of weeks that builds relationships, bridges the gaps that remain and leads to the establishment of a sustainable powersharing executive - one that is built on accommodation and trust, has reconciliation at its heart and is focused on the common good and welfare of all."
The senior clerics said they had met with the five main party leaders last autumn, and were "impressed by the genuine willingness of those involved to engage".
"At the same time, we all need to be realistic about the significant challenges that lie ahead in finding the necessary agreement," they added.
The church leaders said they "notice daily" the "damaging and continuing impact of not having a functioning devolved government".
"Across our community, there is also a growing sense of hopelessness and even despair at the lack of progress," they said.
"For the sake of the most vulnerable in our society, for the sake of the victims of our past, for the sake of children in our schools and for the sake of people who need improved health and social care services, now is the time to find a resolution to the political impasse.
"The Lord Jesus calls us all to go the extra mile for one another and to do what is necessary for the greater good. While the timing for these talks may not be perfect, we believe this to be a fresh window of opportunity, born of tragedy, but nestling in hope for a future that now requires courageous and compassionate leadership."
The statement was signed by the Church of Ireland Primate Richard Clarke, Catholic Primate Eamon Martin, Presbyterian Moderator Charles McMullen, Methodist President William Davison and Brian Anderson, President of the Irish Council of Churches.
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