Peter Robinson and Martin McGuinness have spent their first full day in office together at Downing Street in talks with Prime Minister Gordon Brown.
The agenda included Sinn Féin demands for the transfer of policing and justice powers and DUP concerns about the existence of the IRA Army Council.
The first and deputy first minister both pledged to roll up their sleeves to tackle unresolved business.
Although Mr Brown hosted the talks, he did not chair them.
"While it's good to come here and meet Gordon Brown, the business has to be done back in Northern Ireland"
Mr Brown promised to host the talks after Sinn Féin apparently threatened to derail Mr Robinson's elevation as first minister to succeed Ian Paisley, his predecessor as DUP leader.
On Thursday, at a special sitting of the Assembly, Mr Robinson and McGuinness were appointed first and deputy first ministers.
Irish Minister for Foreign Affairs Micheál Martin was also at Downing Street for the discussions.
On his way in to the talks, Mr Robinson said: "We all have to recognise that while it's good to come here and meet Gordon Brown, the business has to be done back in Northern Ireland.
"That business does not just involve the two largest parties, but the other parties as well. There are a lot of issues that are of deep concern to the unionist community."
Mr Robinson said he had not been aware that an Irish government representative would be at the talks.
"As these are internal Northern Ireland matters, I will be dealing with the British prime minister and the deputy first minister," he said.
However, Mr McGuinness said it was common sense that Dublin was represented at the discussions.
"Both governments were involved in the St Andrews talks and it is sensible in the context of these talks to have all the main players represented," he said.
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