The Minister for Finance has said there is provision in law to give the Government the option to make a change to the appointment of a Central Bank of Ireland (CBI) Governor, in the case of very grave misconduct.

But Paschal Donohoe said he would not make any comment on an investigation underway in New Zealand into the conduct of Gabriel Makhlouf, the incoming boss of the CBI and outgoing New Zealand Treasury Secretary.

Mr Makhlouf's actions and public statements about the causes behind the unauthorised leaking of the New Zealand government's national budget are the focus of an investigation by the country's State Services Commission.

The probe followed an alleged bureaucratic bungle that led to the early release of budget information.

The error resulted in police being called in amid fears the treasury department had fallen victim to a sophisticated cyberattack.

Initially, Mr Makhlouf rejected any suggestion the information had been accidentally posted online.

But he was later forced into a backdown after police found no evidence illegal activity was behind the leak.

Instead, the information was released when the Treasury prepared a "clone" website ahead of the budget release, not realising that entering specific search terms revealed embargoed information.

The opposition National Party, which released the leaked information, called for Mr Makhlouf's resignation, saying he had implied the party was behind an illegal hack.

Speaking to the press in Dublin today, Mr Dohonoe, who appointed Mr Makhlouf last month, was asked whether such an appointment could in theory be undone if he were to feel it had to be.

"The piece of legislation that governs that appointment opens up the option to government to make a change in the case of very very grave misconduct - that is the legislative case and that is the law as it stands at the moment," Mr Donohoe said.

"But I want to make clear two points. The first one is that I'm not going to make any comment on a process underway in another country, and secondly the new Governor of the Central Bank has been appointed under law."

Earlier, Mr Donohoe told the RTE News at One programme that he was very conscious of the need to have utter integrity and utter independence in the Central Bank and added that this is what will happen.

The Labour Party today called for Mr Makhlouf's appointment to be paused, pending the outcome of the investigation in New Zealand.

Mr Makhlouf is due to leave his role in New Zealand at the end of this month and will take up his new position here in September.

Meanwhile, Minister Donohoe said he would bring a recommendation to cabinet in the coming weeks regarding whether or not to vary the cap on bankers' pay and bonuses.

Mr Donohoe said he is well aware of the continued public outrage in relation to the behaviour of the banking sector in the past

But he added that he does believe there have been some important changes.

He said he is considering a report from the Governor of the Central Bank on the matter and when he reaches a final view he will be informing the Cabinet and Oireachtas.

The minister said he would be giving the matter consideration in the context of the past and the present, including the ongoing tracker mortgage controversy.