DUP ministers resigned last week from Stormont in a row over a murder which police think is linked to members of the IRA - a paramilitary organisation that's supposed to have disbanded.
David Cameron's expressed concern about the situation and Northern Ireland Secretary Theresa Villiers was set to reconvene talks between the parties on Monday.
DUP members remained absent as meetings got back underway at Stormont.
Speaking about the crisis Ulster Unionist Party (UUP) leader Mike Nesbitt said: "What we are delivering is broken and it needs to be fixed. We have to return to values and the key value is credibility."
Senior Sinn Fein Assembly Member Alex Maskey said the DUP and UUP should concentrate on solving pressing issues rather than engaging in inter-party bickering. He said: "I am calling on both unionist parties to end their sham fight and have the political will to go into these talks.
Speaking on Premier's News Hour, the Evangelical Alliance's Northern Ireland Director Peter Lynas suggested local people have no idea how this is going to work out.
He said: "There's a lot of confusion here on the ground and more generally - trust and relationship have broken down.
"The shooting is just the climax of the breakdown around welfare reform and some of the budget matters that are actually probably as significant...and then finally that has brought this to a head.
"The feeling on the ground is that people genuinely aren't to sure how this is going to be resolved. There is some concern around that."