The faith leaders spoke to Northern Ireland's main five parties in individual meetings last Friday.
They have called on the UK government to take steps to facilitate the restoration of good governance in Northern Ireland, including the return of fully functioning and resourced devolved institutions.
The statement also asked Westminster to take "all steps possible to meet the outstanding concerns of all political parties, so that each will feel able to return to the devolved institutions."
In a joint statement, the church leaders said they expressed to the politicians the feedback they had received from communities across Northern Ireland regarding "the seriousness of the current situation – indicating the real and sustained financial hardship that is being experienced by many people, combined with the everyday reality that many of the normal services that society depends upon were close to breaking point.
"We also indicated to the party leaders that this was leading to a rising sense of despair, and even hopelessness throughout the community, linked to a growing anger at the current poor state of governance.”
The churches said that although a return wouldn’t be a “panacea”, a properly resourced local government “would make a real and meaningful difference to the everyday lives of people.”
The group is made up of the Church of Ireland, the Methodist and Presbyterian Churches in Ireland, the Roman Catholic Church, and Irish Council of Churches.
Meanwhile, as discussions with the government continue, DUP MP Ian Paisley has blamed the Windsor Framework for its part in "an existential threat facing veterinary and food industry in Northern Ireland". He says the situation has been "exacerbated by the failure of the Windsor Framework to deal with veterinary medicines."
The North Antrim MP said "I had a positive discussion with the director of Food Standards Agency about the need for them to take up the case on behalf of Northern Ireland vets and ensure medicines currently available in NI remain available without any threat to their use."