Mr Gerry Adams and Mr Martin McGuinness held talks yesterday evening with the British Prime Minister as part of the continuing efforts to end the political logjam.
The negotiations, held in Downing Street, were "mostly about policing", according to talks sources.
Talks chiefly involving British and Irish officials, Sinn Fein and the SDLP continue today and are likely to run into the weekend.
Downing Street would not say whether any progress was made. London and Dublin sources said it was important that Mr Blair was in face-to-face talks with Mr Adams and Mr McGuinness, but that there must be further talking before it can be determined whether a breakthrough was possible.
Sinn Fein Assembly member Mr Gerry Kelly said the gap between what republicans were seeking on policing and what the British government was prepared to concede was still substantial.
Mr Kelly repeated that it would be "of no benefit to the process" for the Taoiseach, Mr Ahern, and Mr Blair to come to Northern Ireland with the talks still deadlocked, particularly on the policing issue.
"I would prefer that we get the thing sorted out first and then we talk about how to present it afterwards," he said.
As for the prospects of a deal, Mr Kelly added: "The gap is still substantial. There are very clear areas where we need progress.
"The power to go back to amending legislation is with the British government and Tony Blair. We need to get the thing right. There is no point rushing it," he said. "We will try our very best. We will continue to fight on until we get the police service promised in the Good Friday agreement."
The former IRA prisoner chose the backdrop of the RUC station in North Queen Street in north Belfast yesterday to speak to reporters.
He said people, particularly young nationalists contemplating joining the Police Service of Northern Ireland, wanted a new police service of which they could be proud.
Pointing to the large North Queen Street barracks, he added: "They want an ordinary, run-of-the-mill, small police station which people would be proud to move in and out of. They would be calling the guy or the woman [officer] by their first name, and they would probably be neighbours."
His constituents asked questions about inquiries into killings such as those of Rosemary Nelson and Pat Finucane. They wished to know if officers in the Police Service of Northern Ireland would be using plastic bullets or live rounds.
They also wanted all police officers to take the new human rights oath, rather than just the recruits.
Meanwhile, DUP Assembly member Ms Iris Robinson has claimed she received confidential documents proving the police budget will be cut by over £110 million in the next three years.
This was forcing the RUC to face a series of drastic cuts, including the closure of 15 stations, said the DUP deputy leader, Mr Peter Robinson.
"It is a very dismal picture and one that is bound to start the alarm bells ringing for anybody who is concerned that the guard is being dropped in the battle against terrorism," he added.
The Police Authority chairman, Mr Pat Armstrong, said the RUC Chief Constable, Sir Ronnie Flanagan, had assured him there would be full public consultation before any closures went ahead.
