Peter Robinson and Martin McGuinness have said they have made progress over a budget for policing and justice, following a meeting with Gordon Brown on Monday night.
Meetings on the issue will continue on Wednesday in New York where they are to attend an economic conference.
The talks at Downing Street lasted two and a half hours.
Speaking after the meeting, Martin McGuinness said: "I think we have made significant progress in the course of our discussions this evening about a range of issues that are of concern to us."
Peter Robinson said progress had been made but no overall deal was agreed.
"There is still some work for us to do arising out of the interrogation of the figures that we have been given tonight," he said.
"I think everyone will expect us to do the responsible thing and make sure that the resources are in place before we make any recommendation in relation to the devolving of policing and justice powers."
He added: "These discussions only deal with the financial elements involved in returning policing and justice powers to Stormont.
"Community confidence is the crucial test for devolving these powers and only when the party agrees a final financial settlement can an assessment of community confidence be considered."
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