Sinn Fein President Gerry Adams has met Tony Blair as part of the build-up to next week's talks in Scotland.
Gerry Adams says on-the-runs are a key issue for Sinn Fein
The meeting took place at the prime minister's Chequers country residence.
The governments say agreement is needed on changes to the institutions and support for policing before devolution can be restored.
Mr Adams, who also meets Bertie Ahern on Monday, said Sinn Fein wanted to resolve outstanding issues including policing and on-the-runs at the talks.
Speaking after the Chequers meeting, Mr Adams said the focus of discussions was the restoration of the political institutions.
"There is no more important work in the time ahead for the two governments and the parties than reaching agreement," he said.
"Sinn Fein believes that a deal is possible on all of the issues.
"It will become clear whether or not the DUP are up for an agreement. If they are, the opportunity is there - the way has been cleared."
Asked on Thursday about Sinn Fein's position on policing, he said: "Sinn Fein is for law and order, we are for social justice, we are for decent, accountable civic-controlled policing. Let's get that and then let's move forward."
Earlier this week, DUP leader Ian Paisley said a deal could be reached if Sinn Fein signed up to policing.
Speaking after the Independent Monitoring Commission's latest report said the IRA had changed radically, he said: "If the police question is settled absolutely on a democratic basis and principle we would have come a long way along the road."
Sinn Fein is determined to resolve the issue of republicans who are on the run from police as part of any settlement.
The DUP vehemently opposes any amnesty for republicans on the run from police.
While this may be a deal-breaker for the DUP, Sinn Fein is determined to resolve this issue as part of any settlement.
The British government has laid down 24 November as the deadline for a deal to be reached over the restoration of devolution.
The main parties meet in the Scottish town of St Andrews later this month.
Devolution was suspended in October 2002 over allegations of a republican spy ring.
The court case that followed collapsed and one of those charged, Denis Donaldson, later admitted working as a British agent.