Stormont ministers are set to hold talks with the UK Government over who will foot a potential £1.2bn bill for a delayed Troubles victims' payment scheme.
The First and deputy First Minister, along with the justice and finance ministers, will meet with Secretary of State Brandon Lewis on Tuesday.
It comes as the clock continues to count down on a court deadline for a resolution to the funding impasse.
Deputy First Minister Michelle O'Neill told the Assembly on Monday that ministers had been trying to secure the meeting with Mr Lewis for five months.
She said she wanted the talks to deliver an outcome to the funding dispute.
Earlier this month, the Court of Appeal in Belfast ruled that Stormont was under a legal duty to fund the payment scheme for those who suffered physical and psychological injuries during the Troubles.
It made no finding on the source of that funding and gave the Executive and Northern Ireland Office four weeks to find an agreed solution.
Ms O'Neill said the executive was maintaining its position that the UK Government should fund the new scheme.
During Assembly question time, Ms O'Neill said: "It remains our firm view that the scheme should be funded by the Westminster Government as an addition to the block grant.
"Without additional funding for the scheme through the block grant the Executive will be faced with very significant funding pressures."
Ms O'Neill said the executive would continue to fund required set-up costs for the scheme while the negotiations with Government continued.
She said the remit and costs of the scheme had widened significantly from those agreed by Stormont parties in 2014.
She said the executive had received costing predictions from the Government's Actuary Department based on numbers provided by the Executive Office.
Ms O'Neill said those ranged from £600m to £1.2bn, with a central estimate of £848m.
"That shows the level of challenge which this executive would have to face in terms of trying to fund the scheme, which is why we need the British Government to fund something which they themselves brought forward policy for and took policy decisions on," she said.
The deputy First Minister highlighted that the UK Government's own policy was to fund initiatives it legislated for.
The Government has insisted that the executive needs to pay for the scheme, insisting that it was only legislated for at Westminster because the power-sharing institutions were collapsed at the time.
"The Executive is absolutely committed to paying and delivering upon the scheme - how the scheme is resourced however is a political question and it's a question that needs that urgent focus from the British Government and from Brandon Lewis in particular," Ms O'Neill said.
"It also requires an immediate political solution because, as I've said earlier, victims have had to wait for far too long."
Later, Finance Minister Mr Murphy said: "Clearly those costs make it hugely challenging if not unaffordable for an Executive to carry this burden alone, not to mention the fact that it is contrary to the British Government's own policy, having set the policy and legislated for it," he told MLAs.
Mr Murphy said the Executive paying for the whole scheme will have a "serious knock-on implication for other public services".
"That's not to play off victims and what they deserve and need against public services, because that would be a very cruel thing for the Government to try and do on us," he said.
Mr Murphy said he and his Executive colleagues are committed to ensuring the delivery of the victims' payment scheme, and has allocated £6.7m towards preparation costs for the scheme in the coming year.
"The wider payments issue required urgent attention," he said.
The scheme should have been open for applications at the end of May last year. It was first delayed when Sinn Fein refused to designate a Stormont department to administer it, after objecting to Government eligibility criteria that excluded former paramilitaries convicted of causing serious harm.
Ms O'Neill eventually agreed to nominate a department last August following a highly critical court judgment that found she had been acting unlawfully.
However, the separate stand-off involving the Government and the wider Stormont Executive over funding remains unresolved.
Relatives for Justice chief executive Mark Thompson called on Mr Lewis to stop stalling.
"Across the globe transitional societies have embraced the principle of reparation for conflict harms, yet the Westminster Government has stubbornly refused to act on its obligations to our injured from our recent conflict," he said.
"It has acted particularly perniciously by incorporating numerous discriminations in the scheme regulations.
"It is clear that the scheme requires significant funding that far exceeds block grant capacity.
"It is time for the British secretary of state to sit down and make fiscal commitments to this scheme and put an end to its obfuscation."
A UK Government spokesperson said: "The Secretary of State has been consistent in his support for the Victims' Payments Scheme. He has always been clear that the devolved funding settlement means that the Executive is funded through the block grant, together with its own revenue-raising capabilities to deliver its statutory responsibilities, including this scheme.
"The UK Government has provided unprecedented levels of funding to the Northern Ireland Executive this year. The spending review for 21/22 provides a further increase in funding for the Executive of more than £900m."