Relations between Peter Robinson (left) and Martin McGuinness have soured
Prime Minister Gordon Brown has left Stormont after a series of meetings with Northern Ireland parties on the devolution of justice powers.
Government sources said good progress had been made and Mr Brown would meet the first and deputy first ministers in Downing Street again on Tuesday.
Peter Robinson and Martin McGuinness held separate talks with the prime minister on Monday.
Afterwards, both said the talks had made progress.
"We are calm, we are behaving rationally, we are working through the issues," the DUP first minister, Mr Robinson said.
Sinn Fein's Mr McGuinness said: "In terms of the financial situation, we are moving forward, I think fairly decisively."
The two parties have been at loggerheads over when the powers should be devolved from London.
While Sinn Fein wants it to happen immediately, the DUP is more cautious and has said the transfer of powers will not happen before Christmas.
Mr Robinson said his personal relationship with Martin McGuinness was not a factor in the issue.
"I am prepared and can work with anybody who has the same goals, which are to make the assembly and executive work for the benefit of Northern Ireland."
"I was not elected to be a buddy for Martin McGuinness, I was elected to work with him and that is why I am here."
Mr McGuinness said the prime minister had not put a final figure to him on the cost of a settlement.
"If the British government really want this in place... they will come up with the money. Gordon Brown has reiterated that this will not fail because of money.
"He said he was determined to deliver. We are very rapidly approaching make-your-mind-up time," he said.
Relations between the first minister, Mr Robinson and the deputy first minister, Mr McGuinness, have deteriorated in recent weeks.
Gareth Gordon, BBC News, Stormont
When power was devolved back to Northern Ireland more than two years ago one crucial element was retained at Westminster - policing and justice.
The deal which put old enemies the DUP and Sinn Fein in government together was ground-breaking but most accepted the time was not right to expect them to administer this sensitive area. That has now changed.
The British and Irish Governments, as well as Sinn Fein, believe its time for unionists to agree to "the final piece in the devolution jigsaw."
The DUP says there is not yet sufficient public confidence and that they will only move when there is - there's also the vexed issue of funding.
But Sinn Fein appears to have lost patience, claiming the DUP is using money as an excuse not to do it. With some believing the row is now threatening the stability of the power sharing institutions, the prime minister is hoping he can break the stalemate
Sinn Fein says the transfer of justice powers should have happened months ago, but the DUP says the Treasury must pay for it. The cost is thought to be in the region of £600m.
Mr Robinson has also said the unionist community must have confidence in the new arrangements before he will give the go ahead. He said the transfer could not happen before Christmas.
The Conservative leader David Cameron has said if he becomes prime minister it would be his inclination to support whatever budget is agreed for devolving policing.
He said the Conservatives are committed to devolution - and the uncertainty over the budget could be helped if the government talked to him about it.
Last week he told the BBC: "We want it to happen and generally speaking commitments that are made we will try and agree to, but I can't give a blank cheque."
BBC NI political editor Mark Devenport said Monday's talks were part of a series of meetings and no-one is expecting any kind of historic agreement on Monday.
Childcare protesters met Mr Brown at Stormont
"What they say they have been doing is slowly narrowing down the issues in relation to finance," he added.
"There are a few complicating factors, one is that some of the financial estimates are a bit fluid."
Our correspondent said there could be difficulties "further down the road" if Sinn Fein was to conclude that the unionists were going to delay indefinitely on the matter.
"Lurking in the background is the thought - what if Sinn Fein were to try to pull the plug on the executive or trigger an early election?
"Nobody is certain at this stage whether they might do that or not."
Mr Brown was met by demonstrators protesting about childcare vouchers as he arrived at Stormont in a convoy of about 10 vehicles accompanied by motorcycle outriders.