The Tanaiste, Ms Harney, offered to resign from office, last Tuesday, because of her involvement in the decision by Judge Haugh to postpone indefinitely the trial of Mr Charles Haughey.
Had her offer been accepted, it would almost certainly have brought down the Coalition Government, precipitated a general election and caused a leadership crisis within the Progressive Democrats.
Ms Harney's comments that the former Taoiseach should be jailed was quoted as a major reason for the postponement of Mr Haughey's criminal trial on a charge of obstructing the McCracken tribunal.
That decision has since been appealed to the High Court by the Director of Public Prosecutions.
Immediately on her return from Poland last week, the Tanaiste offered her resignation to the Taoiseach, Mr Ahern.
She was said to have been "very cut up" by Judge Haugh's ruling and felt that the matter of her involvement had to be addressed directly.
A spokesman for Ms Harney said the Taoiseach had refused to accept her resignation at a pre-Cabinet meeting when they had discussed the matter.
The Coalition Government was under intense and growing pressure at the time as the Dail moved towards its summer recess.
Later in the day, Ms Harney raised the issue of her continuing leadership of the Progressive Democrats with three or four senior colleague, including Minister of State Ms Liz O'Donnell and Mr Des O'Malley.
They were said to have strongly dissuaded her from resigning.