Peter Robinson is stepping aside to clear his name
Gordon Brown has urged Northern Ireland politicians to remain focused on the issues of government, despite problems surrounding DUP leader Peter Robinson.
The first minister has stood down for six weeks to fight claims over his wife's financial dealings - Enterprise Minister Arlene Foster has taken over.
But the power-sharing executive's future remains at risk over devolution of justice and policing powers.
The DUP and Sinn Fein have held talks over the issue with more due later.
In a statement, the British prime minister said: "I urge all politicians in Northern Ireland, whatever the turbulence of recent events, to remain focused on the business of government, and to recognise the crucial importance of intensifying engagement in those issues which remain to be solved."
Mark Simpson, BBC Ireland correspondent
The focus in Northern Ireland is shifting.
For the past week the spotlight has been on Peter Robinson, his wife, her teenage lover and a controversial business deal.
Now attention is moving onto Stormont's key political relationship - the power-sharing pact between Sinn Fein and the DUP.
It's been in trouble for months. And now matters are coming to a head.
The parties are arguing about when policing and justice powers should be transferred from Westminster to Stormont.
But at the heart of the dispute is a fundamental question - are the DUP and Sinn Fein still capable of working together? If not, the Stormont Assembly will soon collapse.
The parties held private talks at Stormont last night, but there was no sign of any progress.
He added that he had spoken to Arlene Foster on Monday evening.
Irish Prime Minister Brian Cowen welcomed Mr Robinson's decision to continue work on what he called the crucial issue of the devolution of justice and policing powers.
The DUP and its main coalition partner Sinn Fein have been at loggerheads in recent months over the devolution of policing and justice powers from Westminster to the Assembly in Belfast.
Sinn Fein wants the powers transferred immediately while the DUP has said there needs to be greater community confidence before devolution can happen.
Secretary of State for Northern Ireland Shaun Woodward said he was confident that talks between the DUP and Sinn Fein would continue and said there had been three "lengthy" meetings on Monday.
"To be fair to Peter Robinson, he's actually as good as his word on this and engagement is taking place and there will be more meetings tomorrow and throughout this week," he told BBC's Newsnight.
Mr Robinson is facing a claim that he knew his wife obtained £50,000 from two developers for her teenage lover but did not tell the proper authorities.
Arlene Foster is beginning her first full day as acting first minister
Iris Robinson, an MP and an NI Assembly member, is currently receiving "acute psychiatric treatment" following a BBC Spotlight documentary broadcast last week.
It reported that she obtained £50,000 from two property developers for her 19-year-old lover, Kirk McCambley, to open a cafe.
She failed to register the money with authorities in Stormont and Westminster, as required by law.
A BBC Panorama programme reported at least £5,000 of the money received by Mrs Robinson's young lover has not been paid back to a property developer.
It has been announced that she will step down as an assembly member and MP this week due to ill health. Sources have also confirmed that she will be leaving the DUP.
The DUP assembly team has said it offered Mr Robinson its "wholehearted support".
Other NI political parties seemed less than convinced by the DUP's shuffling of its decks.
The Northern Ireland Assembly is to investigate the conduct of both Robinsons.