British Prime Minister Tony Blair and his Irish counterpart Bertie Ahern, seeking to broker a deal before a November deadline, held an opening plenary session followed by bilateral talks with party leaders late on Wednesday.
On Thursday they are likely to get into tougher areas as they battle to hammer out an agreement before the end of the crunch closed-door talks on Friday.
"I think its a good mood. People are setting out their positions as expected. We're now getting down to the nitty gritty," said Irish Foreign Minister Dermot Ahern after the first session.
A spokesman for Mr Blair said that, after the initial plenary and bilateral format talks, there was no pre-defined structure for discussions from Thursday.
That will allow Mr Blair and Mr Ahern the freedom to broach the key issues as they see fit.
Mr Blair and Mr Ahern are hosting three days of talks between leaders from both sides of the divided province: republicans who want to unite with Ireland, and unionists demanding to stay part of the United Kingdom.
Britain, which suspended a power-sharing government based at Stormont Castle outside Belfast four years ago, insists that failure to strike a deal before a November 24 deadline will see it closed indefinitely.
Dealing with Sinn Fein
Pressure will notably focus on firebrand Protestant leader Reverend Ian Paisley, who rejects sharing power with the republican Sinn Fein until its military wing, the Irish Republican Army (IRA), definitively gives up the gun.
Mr Paisley, known for his fiery rhetoric often aimed at Catholics, sounded in a compromising mood as he arrived. "We are not here to argue with Sinn Fein or to debate with Sinn Fein," he said.
"We're here to listen, if they're going to deliver," he told reporters.
But Sinn Fein's chief negotiator Martin McGuinness, speaking after the first session, sought to keep the pressure squarely on Mr Paisley.
"We're off to a good start," he said, but added: "It really comes down to whether or not Ian Paisley is going to deliver his constituency and his party for a deal. I hope he's up for it."
Mr Blair and Mr Ahern helped hammer out the landmark 1998 Good Friday agreement.
That ended some three decades of so-called Troubles which left over 3,500 people dead, many at the hands of the IRA.