The banks are expected to issue statements later this week which will give details of how they will tackle the tracker mortgage issue.
It is understood the statements will outline details of what they have done to date.
The statements will also outline how much more work the banks will do on the issue.
Minister for Finance Paschal Donohoe held a series of meetings with senior representatives of KBC, Bank of Ireland and Permanent TSB, to discuss the tracker scandal.
He also will meet Ulster Bank and AIB over the next two days.
The Minister is expected to publicly address the issue on Wednesday when he finishes his final meeting with the banks.
A spokesperson for Mr Donohoe said the Minister found it "very disappointing that despite the significant management and board changes that have taken place since the onset of the financial crisis that there still seems to be a cultural issue with some of the banks."
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It is understood that this evening, Mr Donohoe told his Cabinet colleagues that he expects clarity this week from the banks.
At a Cabinet meeting, he told Ministers that he wants the remaining groups of mortgage holders resolved and a timeline put in place.
He said that 7,000 mortgage holders have been compensated while there is agreement between the banks and Central Bank that another 13,000 need to be resolved.
The Minister also said full agreement had not been reached between the Central Bank and banks on another 7,000 mortgage holders.
Sources say the Minister told the Cabinet meeting there would be clear consequences if there was a lack of action.
Earlier, the Governor of the Central Bank said the vast majority of the 13,000 customers who were wrongly taken off their tracker loans would be repaid by Christmas.
Philip Lane said the next step would be to make sure more customers would be included in the investigation.
He was speaking following talks with Mr Donohoe.
Tracker scandal: 'Vast majority will be paid out before Christmas,' Central Bank Governor Philip Lane says pic.twitter.com/cuDeqP3P3z— RTÉ News (@rtenews) October 23, 2017
When asked about the suggestion that the Central Bank could lose its consumer protection mandate, he said that the bank remained fully engaged in its consumer protection mandate, "which is at the heart of its work".
He said banks had paid out €160m already, but this only represented a fraction of cases. He said he did not want to say how much the final cost would be for the banks.
The meeting came ahead of Mr Donohoe's meetings with the CEOs of KBC Bank and Bank of Ireland this morning on the tracker loan scandal.
Both banks are seen as having big questions to answer.
Upon leaving today's meeting, the Chief Executive of KBC Bank Wim Verbraeken said the Minister had conveyed the Government's grave concerns.
He said the bank would make a full statement later this week.
Bank of Ireland's CEO Francesca McDonagh also said the bank would make a statement in due course.
The Minister also met Permanent TSB this afternoon.
Lane's statement over tracker mortgage customers welcomed
Financial advisor Padraic Kissane, who has been assisting many of those who were wrongly taken off tracker mortgages, has welcomed the statement by Mr Lane that the vast majority of customers would be repaid before Christmas.
Speaking on RTÉ Six One News, Mr Kissane said that he has seen no change in the attitude of the banks in his dealings with them in recent weeks.
He said he has made a lot of constructive progress with AIB, but said that this is the only bank he could say this about at present.
Mr Kissane said that internationally, the reputation of Ireland's banks is being destroyed and that at a time when Brexit is occurring, the restoration by the banks of their reputations should be the challenge of every lender.
The Government has threatened to impose sanctions on the banks, including fines, extra taxes, or more regulation, if they do not make substantial progress on the issue before Christmas.
Speaking today, Taoiseach Leo Varadkar reiterated that the Government would take further action if the banks did not act.
The handling of the scandal by the Central Bank has also come under the spotlight, with the Government examining the possibility of removing consumer protection functions from the Central Bank and establishing them independently.
Mr Varadkar said no decision had been made on it yet.
However, there was general consensus at this evening’s Cabinet meeting against separating consumer regulation from the Central Bank.
It was felt that the Central Bank has a lot of power and a new agency would be less powerful.
Mr Donohoe said that he was broadly considering accepting Fianna Fáil's motion on tracker mortgages, and he would be in discussions with Fianna Fáil on the issue.
Fianna Fáil's Finance spokesperson Michael McGrath has said the number one priority in the scandal should be that customers who have been identified as being affected, should get their money back as quickly as possible.
Speaking on RTÉ's Morning Ireland, he said affected customers should be repaid by Christmas.
He said this should be possible, pointing out that AIB has refunded 97% of customers who were identified as victims of the problem.
The Cork South-Central TD said the State's first priority should be the customers and should not be coloured by the fact it has stakes in some banks.
Mr McGrath said the Minister for Finance needed to tell banks to "get on with it" and said there were measures the Government could introduce to force the banks to move forward. This included introducing legislation to allow class actions, he said.
Mr McGrath also said the Central Bank should be given more resources to deal with the banks on this issue.
Speaking on the same programme, Fine Gael Senator Kieran O'Donnell said the scandal had "dragged on too long" and there was no reason why victims could not be compensated by the end of the year.
Mr O'Donnell, who is a member of the Oireachtas Finance Committee, said there were a range of actions and sanctions the Government could impose on banks if victims were not compensated.
The Central Bank has responded to suggestions that the Government may remove its consumer protection functions by saying the tracker probe is evidence of its using that mandate.
Junior Finance Minister Michael D'Arcy told RTÉ's 'This Week' programme yesterday that "removing the consumer protection section from the Central Bank and establishing it independently" was one of the options being considered by the government.
A spokesperson for the Central Bank told RTÉ News that it works at all times to fulfil the twin mandate given to it by the Oireachtas of safeguarding stability and protecting consumers, and it applies itself to both "with equal force".
"Through our work to protect consumers, people can be reassured that the Central Bank is working in their best interests by requiring that lenders identify all customers affected by tracker mortgage issues, at any time in the past, and to provide appropriate redress and compensation without delay," they said.
"The Central Bank has forced lenders to deliver €163m in redress and compensation to date for affected customers and much more will follow, combined with further enforcement actions to punish banks for wrongdoing."
He stated that the examination of the tracker issue "is evidence of our consumer protection mandate in action".