Mr Ahern and Mr Blair met at Downing Street
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Ongoing IRA activity is the "obstacle to a lasting and durable settlement in Northern Ireland", Tony Blair has said.
He was speaking after meeting Bertie Ahern at Downing Street on Tuesday to assess their political options in the wake of the £26.5m Northern Bank raid.
Chief Constable Hugh Orde and Garda Commissioner Noel Conroy updated them on the latest security assessments.
This included the state of the investigation into the Belfast robbery, which has been blamed on the IRA.
Ceasefire report
The Independent Monitoring Commission's report on the robbery is expected to be sent to the governments this week.
The ceasefire watchdog's report is expected to confirm the police assessment that the IRA was behind the raid, and to recommend certain sanctions.
The two prime ministers' meeting was seen as their most significant since they launched their joint proposals for the restoration of devolution in Northern Ireland in December.
After the meeting, Mr Blair said: "The obstacle now to a lasting and durable settlement in Northern Ireland is the continuing paramilitary activity and criminal activity of the IRA."
"It has got to stop and it has got to stop in its entirety. There cannot be any compromise with that.
"If it is given up definitively and completely, the process can move forward on an inclusive basis."
More than £26m was stolen from the Northern Bank
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He added: "For several years, people were prepared to see a process of transition take place.
"That is now over, as far as everybody is concerned - north and south of the border, everybody is of the same view."
SDLP leader Mark Durkan also held talks with Mr Blair on Tuesday, while the DUP met Northern Ireland Secretary Paul Murphy.
Mr Durkan said: "Our strong message to him was that there could be no more tolerance of any activity from any group, loyalist or republican, at any time.
"We argued with him that this was vital to stop the mafia culture spreading throughout our society."
The two governments have been considering their strategy for the coming year.
It is understood they believe an all-inclusive executive is impossible without a complete end to IRA activity.
Garda intelligence
The four Independent Monitoring Commissioners have held recent meetings with the chief constable and the garda commissioner, as well as extensive high-level meetings with British and Irish Government officials.
There has been speculation that their report will be published next week.
BBC Northern Ireland political editor Mark Devenport said some form of sanctions appeared likely in the short term.
He added: "But so far as the bigger picture is concerned, most observers would be sceptical about the chances of any real movement this side of the next general election."