The banking inquiry will be completely independent of the Cabinet and will not operate under Government instruction, Taoiseach Enda Kenny has said.

Speaking in Lebanon today, where he is visiting Irish peacekeeping troops, Mr Kenny also said Independent TD Stephen Donnelly should reconsider his decision to resign from the inquiry, adding that the Wicklow TD had a "lot to offer".

As the row continued over the Government move to add Labour and Fine Gael senators to the committee, which prompted Mr Donnelly's resignation, Mr Kenny said the inquiry "does not operate to a mandate or direction or instruction from Government".

The Government yesterday announced that the party whip would not apply to any Fine Gael or Labour member of the committee.

“Fine Gael members who attend on the committee have absolute freedom in the context of working with the committee as to what they want to do,” Mr Kenny said today.

Mr Donnelly this evening said he had heard nothing to make him change his mind about withdrawing from the committee. He said public trust in the process was crucial and that this had been “destroyed” by the Taoiseach’s intervention last week.

“Nobody I have spoken to believes [the committee]will be able to do its work in an unbiased, non-political way,” he told The Irish Times. “The two senators forced on to the inquiry should step down… There’s no point to the work if the public think it’s a political exercise.”

Minister for Finance Michael Noonan earlier defended the Government's handling of the inquiry, saying a "stroke" pulled in getting Opposition senators on to the panel and had been reversed by the addition of Coalition members.

Speaking in Limerick, Mr Noonan said "strokes" such as the Government seeking to regain a majority on the inquiry were often pulled in Leinster House.

"Fianna Fáil pulled a stroke because Labour Senators were absent and fair dues to them. The stroke is now being reversed," he said.

Senior Fine Gael and Labour members today criticised Fianna Fáil's approach to the inquiry. Tánaiste Eamon Gilmore said the party appeared to be seeking to halt the inquiry, an allegation rejected by Fianna Fáil members.

Mr Gilmore said he believed some people had “an interest in making sure that there isn’t a banking inquiry” and he believed “first to the table on that” is Fianna Fáil. “They don’t want a banking inquiry at all,” he told reporters in Dublin.

He was responding to a suggestion from Fianna Fáil leader Micheál Martin, who said that the public was losing confidence in the investigation.

Fianna Fáil finance spokesman and inquiry member Michael McGrath TD rejected Mr Gilmore’s assertion, describing it as “a political claim”. He accused the Government of “trying to dig itself out of a hole it has created in relation to the inquiry” through “political meddling” which he feared had damaged the credibility of the entire process.

Mr McGrath said Fianna Fáil had made it clear it would fully co-operate with the inquiry even though it did not believe it was the best approach to the issue as it would be unable to make findings against individuals or organisations involved in the State’s banking collapse.

“The Government now is trying to throw as much mud as it can in the hope it will stick whereas in truth the damage to the inquiry was caused directly by its own action,” he told The Irish Times.

Mr Noonan said Mr Martin had tried to turn the move to add Government members to the inquiry into a matter of great principle. Asked why the Government was so keen to have a majority on the inquiry panel, Mr Noonan replied that committees always reflect the strengths of the various parties in the Dáil.

“It’s not a huge issue and I hope now that the members of the committee will get down to doing what they were selected to do.”

Speaking on RTÉ's Morning Ireland today, Mr Martin predicted that if a general election was called, the banking inquiry would collapse, whereas if a judicial inquiry was taking place outside the Oireachtas it would not do so.

“I’m at a loss as to why the Government will not go back to the drawing board given the mess it has made of this particular inquiry,” he said.

A judicial investigation modelled on the Leveson inquiry into the British press would be “cheaper, faster, more effective”, he said.

Asked about what kind of inquiry should be established, Mr Noonan replied that it was important that politicians, as the representatives of the people who spoke “long and loud” about the banking crises prior to the election, would be involved in the inquiry.

“The alternative is to give it to a judge and while judges do great work and have done good work in inquiries in the past, I think there is a necessity here for the public through their representatives to establish the facts.”

Mr Donnelly announced his resignation from the inquiry yesterday in protest at the Government’s decision to restore its majority on the committee, which he said “clearly subverted the democratic process” in the Oireachtas.

Minister for Transport Leo Varadkar today said that Mr Donnelly's resignation was a mistake. "I can totally see where he's coming from but I think he's made an error in judgement," he said.

Mr Varadkar said he hoped the public had not lost faith in the credibility of the banking inquiry following the controversies last week. He said the decision that a party whip would not apply to any Fine Gael or Labour member on the committee should reaffirm the credibility of the investigation.

Mr McGrath said he could not see what difference the party whip not being applied in the inquiry would make, as influence from Government can be “exerted in very overt ways or very subtle ways”.

“The proof will lie in the way members conduct themselves and if they are willing to include in terms of reference decisions made by the current as well as previous government,” he said.

Meanwhile, former Fine Gael TD Peter Mathews has renewed his appeal for a place on the banking inquiry.

An Opposition-backed attempt to have the former financial consultant included on the committee was last month voted down.

“What happened last week was shambolic and shameful. The committee should comprise a number of people who are experienced and suitably qualified,” Mr Mathews said.

Mr Mathews said he was being stopped in the street by people telling him he should be on the banking inquiry. However, he would not be prepared to join the committee unless Mr Donnelly was re-appointed.