Ms Beverley Cooper Flynn's personal statement to the Dáil merits further examination, the Labour Party said last night.
Postponing a final judgment on the statement for now, Labour said the Mayo TD's statement had been technical and detailed.
"But at the end of the day it is the tribunal that will have to delve into what she claimed today. They are the only ones who can determine the veracity, or otherwise, of the statement," said a spokesman.
Adopting an equally cautious approach, Fine Gael said her Dáil contribution had "helped to clarify matters in this instance", but other questions remained.
Her employer at the time, National Irish Bank, is the subject of a High Court inspectors' report, which is now due to be published by the summer.
Furthermore, remarks in the Dáil by the Taoiseach, Mr Ahern, raised questions about his handling of Ms Cooper Flynn's readmission to the Fianna Fáil parliamentary party before the last general election.
"He avoided answering the question as to whether he had sought assurances from Ms Cooper Flynn as to whether she had ever been involved in, or facilitated tax evasion schemes before she was readmitted," said a Fine Gael spokesman.
Fianna Fáil colleagues last night believed that she had ensured that the Parliamentary Party would take no action against her in the short term, though there was little likelihood of that happening anyway.
"It was very carefully written. It will be parsed and analysed over coming days to see if there are any gaps. It doesn't answer all of the questions, but I don't think that anybody will blow a hole in the bits that she did say," said one colleague.
