He said this was to prevent a vacuum that could be filled by dissident republican groups.
Unionists are prepared to bring down Northern Ireland's power-sharing government over claims the Provisional IRA still exists.
It follows Kevin McGuigan Sr's murder in east Belfast, earlier this month.
Mr Ahern, who was a key player in the Northern Ireland peace process, told The Irish Times "it was a time for cool heads".
"The bigger picture is the ongoing peace process," he said.
"It is always delicate. Cool nerves, think this through.
"It is terrible there are atrocities, but are those atrocities being done [by people] who might have been on the inside but are now long since on the outside?
"Unfortunately, there are always fringe players in the organisations.
"People should keep it calm. We should never get lax about the bigger picture, and we should just keep that to the forefront and not talk ourselves into crisis. There is a bigger picture; the bigger picture is the ongoing process.
"These peripheral things, which I can only assume are not sanctioned, are going to continue to be a difficulty. That is something that has to be addressed."
Earlier this week, former Irish justice minister Michael McDowell said the Irish and British governments had allowed the Provisional IRA to continue as an "unarmed and withering husk".
This was because the governments feared a dissident group would fill the void left if the PIRA disbanded.
Mr Ahern said he agreed with Mr McDowell's assessment.
"We should always remember that there [is] a small dangerous group who do not want to see the spirit or the progress of the Good Friday Agreement implemented," he said.
"Nothing should be done that creates a vacuum that allows them to expand and grow."
Mr Ahern said it was envisaged that the Provisional IRA would develop along the lines of the old IRA and they would continue holding peaceful commemorations.
Former Irish Prime Minister Bertie Ahern has said it was envisaged the Provisional IRA would remain as an unarmed group.