Sinn Fein leaders Gerry Adams and Martin McGuinness hold talks with David Cameron
Sinn Fein leaders Martin McGuinness and Gerry Adams have held talks with David Cameron at Westminster.
Speaking after the private meeting, Mr McGuinness, Deputy First Minister of Northern Ireland, said the conversation had been "very forthright" on both sides.
He insisted Mr Cameron would need to give a "powerful input" in order to find a solution.
"I believe it was a very important meeting... there are huge challenges to be faced," he said.
"Our discussions dealt with those challenges, they dealt with the situation in regard to welfare, the situation in regard to the Comprehensive Spending Review and how that will impact on our institutions over a number of years.
"I think that the big challenge over the course of the next very short while is to try and get to a solution. Whether or not that is achievable, I think it is going to take the will of all of those who are charged with the responsibility of finding a solution."
Mr McGuinness said the idea of taking welfare powers back to Westminster was "absolutely unacceptable" to Sinn Fein.
Mr Adams added: "We started a conversation today and that conversation will continue."
Meanwhile Stormont's Finance minister has warned that a £600 million black hole in Northern Ireland's budget is set to increase by "hundreds of millions of pounds" with the latest round of welfare reforms at Westminster.
Arlene Foster said the financial consequences of the UK Government's further changes to the benefits system reinforced the need for the powersharing administration in Belfast to finally resolve its long-running impasse over welfare.
The devolved five-party mandatory coalition has agreed a spending plan for the rest of 2015/16 that, at present, has a £600 million funding gap - in large part down to the failure to introduce last year's Stormont House Agreement.
The agreement between the Executive parties and the British and Irish governments has been held up due to deadlock over the implementation of the last Tory/Lib Dem administration's welfare reforms in Northern Ireland because of a Sinn Fein/SDLP veto.
The Treasury is currently taking around £10 million a month from the Executive's funding to reflect the fact it is still operating the old, more expensive welfare system.
Mrs Foster said the roll-out of the government's latest benefits reforms will have an even greater impact on the administration in Belfast, if the Executive fails to reach an agreement on welfare.
The minister said the £600 million gap in the budget was now going to significantly increase.
"It will have increased as a result of what's happening at Westminster," she said.
"We haven't been told the full scale of that yet, but it will be in extra hundreds of millions of pounds. So this is even more pressure to have this dealt with and dealt with quickly."
The DUP opposed the Welfare Bill as it passed its first stage at Westminster last night. The party's East Antrim MP Sammy Wilson delivered a bleak assessment during the debate when he predicted the legislation probably "spells the end of the Northern Ireland Assembly".
Mrs Foster said her party colleague was stressing the need for a resolution.
"I think Sammy is reflecting the fact that we just can't keep on the way we are going and thinking, Micawber-like, that something will turn up," she said.
"Something is not going to turn up; we are going to have to deal with this issue, and frankly, if we don't deal with this issue then Westminster as the sovereign parliament will step in and deal with it."
The DUP has called for the Government to legislate for welfare changes in Northern Ireland above the head of the Assembly.
Such a course of action would, however, run the risk of Sinn Fein walking away from the administration - a move that would automatically trigger the collapse of the institutions.
The Treasury has already given the Executive a formal warning that it is engaged in preparatory work to take control of its finances if it overshoots its spending limits.
Chief Secretary to the Treasury Greg Hands has written to Mrs Foster making clear that an intervention would happen if the current budgetary crisis is not resolved.
The welfare deadlock has put the rest of the measures contained in the Stormont House deal on hold.
Those include the devolution of corporation tax powers to Belfast, access from the Treasury to £2 billion of additional spending powers, a major civil service redundancy scheme and new institutions to deal with the thorny legacy of the Troubles.
While initially voicing support for the overall Stormont House Agreement, Sinn Fein later withdrew backing for the welfare reform section - claiming proposed Executive-funded top-up schemes for claimants were not as comprehensive as they envisaged.
The SDLP is also opposing the welfare reforms, but Sinn Fein's position is more crucial, as it has the electoral strength in the Assembly to make or break the Stormont House deal.