Leaders of the five Executive parties are expected to meet this week to discuss welfare reform.
Northern Ireland Secretary Theresa Villiers will chair the talks.
She said: “I believe that all sides accept we need to find a way through this and see the Stormont House Agreement fully and faithfully implemented.
“Over the last three days, the Executive parties have been involved in intensive discussions on this and I hope to chair another leaders’ meeting this week to assess progress.”
The row over welfare reform erupted when Sinn Fein made a shock announcement hours before a final Assembly debate.
It centres on whether Stormont-funded mitigation schemes designed to support those in the Province who lose out under the reformed UK welfare system will cover future claimants, not just existing ones.
Sinn Fein pulled support after alleging the DUP acted in bad faith by proposing to limit the schemes to current claimants.
The DUP has insisted there was never an agreement to support future claimants and said such a system would require another £286 million.
Implementing the Government’s changes to the benefits system is a key plank of December’s landmark Stormont House Agreement which was agreed after 11 weeks of intensive negotiations.
Without the long-delayed legislation passing, the whole deal would probably implode and the future of the power-sharing institutions would be plunged into uncertainty.
Ms Villiers has warned that without agreement on welfare the budget would be unsustainable and the devolution of corporation tax powers would be put in jeopardy.
In Washington DC she said tax powers were due to complete their journey through Parliament on Tuesday.
“There can be no doubt that the decision of Sinn Fein and others to block the final stage of the welfare reform Bill in the Assembly was a major setback.
“I’m afraid there’s no room for ambiguity. Implementation of the welfare reform package is a key part of the Stormont House Agreement.
“Failure to resolve this could have profound implications. Without welfare reform the Executive will enter the new financial year in a few weeks’ time with a budget that simply doesn’t add up.
“We would be right back in the same crisis position we were last autumn, with the prospect of the Executive starting to run out of money and facing an existential crisis.”
She warned all the other elements of the Stormont House Agreement would fall if the welfare aspects are not implemented, including the structures on the past, the financial package and corporation tax devolution.
“The consequences could be dire and should that prove inconclusive, even see the collapse of devolution altogether.”