Invitations have been issued to Taoiseach Leo Varadkar and Minister for Finance Paschal Donohoe to appear before the Oireachtas finance committee in relation to the tracker mortgage controversy.
It was confirmed this evening by Chair of the committee Fianna Fáil's John McGuinness.
Speaking in the Dáil, Mr McGuinness called for the consumer protection function to be removed from the Central Bank, who he accused of "standing idly by".
He said the banks had robbed individuals and families of everything, including their dignity and he accused the minister of driving the getaway car for the banks.
It came as the Dáil debated a Fianna Fáil motion on the controversy, which included a call to provide a detailed explanation on how the issue occurred in the first instance.
Proposing the motion, Fianna Fáil's finance spokesman Michael McGrath said an unknown number had been living with this nightmare for as long as a decade.
He said some banks were threatening the Central Bank with legal action, and the Central Bank itself could have done better to deal with the issue.
An amended motion was carried without a vote.
Sinn Féin’s finance spokesperson Pearse Doherty has said that there needs to be accountability to find out why the banks individually and collectively took their customers off the tracker mortgage rates for a long period of time.
He was speaking after all five banks caught up in the tracker mortgage issue - AIB, Bank of Ireland, Permanent TSB, Ulster Bank and KBC Bank Ireland - provided updates on their progress in offering compensation and redress to affected customers.
Minister Donohoe described the behaviour of the banking sector in relation to tracker mortgages as "disgraceful and a scandal."
Mr Doherty said that some Ulster Bank customers will have to wait up to eight months to get money back which was wrongly and unlawfully taken off them.
He said there was nothing in the Minister's statement to the fact that Permanent TSB was currently putting tracker mortgage victims back on to the wrong rate.
Mr McGrath said that he does not believe we have got the full story in relation to the extent of the tracker mortgage problem or why it happened in the first place.
Speaking following the statements by the banks, Mr McGrath said that yet again those caught up in the scandal had been badly let down.
He said unless there was further intervention the issue would run and run well into 2018.
He said the banks did not have a handle on the problem yet.
Meanwhile, People Before Profit TD Richard Boyd-Barrett said the banks cannot be trusted and there should be criminal prosecutions against those responsible for the tracker mortgage controversy.
He said apologies, statements and promises were not enough, and there needed to be heavy sanctions imposed on the banks.
Mr Boyd-Barrett said we needed to move on now to look at the rip-off of variable rate customers by the bankers, and we needed to abandon a government policy of treating banks with kid gloves.
Labour TD Jan O'Sullivan said it was clear the behaviour was endemic in banks, but we still do not know how it happened.
Ms O'Sullivan said the banks had perpetrated a grave act of betrayal of their customers.
"We have yet to be told why it happened. To the outside observer the pattern would indicate a conspiracy to remove contractual obligations from customers," she said.
Earlier, the Independent Alliance called for tougher measures to deal with banks on the issue.
The Minister of State for Training, Skills, Innovation, Research and Development, John Halligan, called for an independent body to deal with compensation, because he said the banks "can not be trusted" in that regard.
He also called for a criminal investigation to take place because he said the banks took money fraudulently from people.
"It has to be investigated and there should be a criminal investigation", he said.
Minister for Transport Shane Ross said the Independent Alliance is of the view that the banks have "gone rogue" in a market that is not operating properly.
The minister described the suffering of people on tracker mortgages as "unacceptable".
He said the group is suggesting that the time for playing and relying on "vague aspirations of moral suasion" by the Central Bank is over.
"They don't have morality, they don't respond to moral suasion and we'll support any tough measures taken by the Minister for Finance today and playing hard ball with the banks", he said.
Yesterday, Mr Donohoe told the Dáil that the Government is not satisfied with the progress made to date by the banks on the issue and said customers had been treated "disgracefully".
He met AIB and Ulster Bank yesterday and both banks apologised for their role in the tracker mortgage scandal.
He held talks with Bank of Ireland, Permanent TSB and KBC on Monday.