Democratic Unionists and the SDLP say they are convinced that top-level republicans were behind last month's £26.5 million bank robbery in Belfast.
They were speaking yesterday after the Chief Constable, Mr Hugh Orde, had briefed a private meeting of the Policing Board, which runs the PSNI.
According to representatives from both parties, they are now more confident that Mr Orde's assessment that the IRA was responsible is correct.
The Irish Times understands that Mr Orde went so far as to admit that if he is proved wrong his tenure of office is finished.
Mr Alex Attwood, the SDLP Assembly member for West Belfast, said: "On the basis of what he confirmed to the board today I . . . have no doubt his attribution in relation to this matter was correct."
He also said that the claim by the Taoiseach, Mr Ahern, who said senior members of Sinn Féin would have had prior knowledge of the robbery was also correct. "I am convinced that senior people in the republican movement knew, or had to know, about what was happening," he said, "both those on the IRA side and those who position themselves as political representatives."
Mr Sammy Wilson said: "The one thing that was clear from the briefing given was that this would not have been done by people who were low-level operatives, nor indeed would they have taken the risk if it had not been sanctioned from higher up."
It is understood the PSNI bases its assessment, not just on its own intelligence source, but also on information supplied by the Garda.
One senior police source said: "We have been working with the Garda since day one in this investigation. We have built up a very close working relationship with the Garda over many years."
The highly-reliable source added: "The Garda is assisting us in many ways in relation to the van [used to transport the £26.5 million from the bank], the possible surfacing of the money - all sorts of aspects like that. This is very much a live and ongoing inquiry."
Police now have more than 1,000 active lines of inquiry, and a significant advance has been made in relation to one of them within the past 36 hours.
Sir Desmond Rea, the Policing Board chairman, said the briefing given by Mr Orde and the Assistant Chief Constable, Mr Sam Kinkaid, had gone into significant detail about the status of the investigation.
"Members, I believe, will leave the meeting much more informed," said Sir Desmond. "They will very much adopt the position that the Police Service of Northern Ireland should have the space to get on with the investigation."
Sinn Féin continued to call on the PSNI to produce its evidence for the contention that senior republicans were behind the theft.
Mr Gerry Kelly, the party's policing spokesman and North Belfast Assembly member, insisted that nothing new had emerged to put the IRA in the frame for the robbery.The emphatic restatement by the PSNI of its assessment of responsibility for the robbery, and the indication that intelligence sources in the Republic supported that view, sets the scene for a key meeting between the Sinn Féin president, Mr Gerry Adams, and the Taoiseach next Tuesday.The Independent Monitoring Commission, which reports on paramilitary activity, is now expected to produce another assessment soon.