Taoiseach Brian Cowen and Green Party leader John Gormley met for 50 minutes in Government Buildings this afternoon and discussed the proposed banking inquiry.
A spokesperson for the Green Party said some progress was made and described the meeting as a 'good one'.
The precise nature of the inquiry will be set out by the Government tomorrow following a Cabinet meeting.
Earlier, Green Party Senator Dan Boyle said he hopes the proposed banking inquiry will be held in public.
Speaking on RTÉ, Senator Boyle said the structure and length of the inquiry still had to be decided. 'As far as the Green Party is concerned, it needs to be open, it needs to be time-defined and needs to have Oireachtas involvement,' he said.
Opposition parties have said it is essential the inquiry should hold bankers to account in public to restore confidence in the banking system.
The leader of the Labour Party, Eamon Gilmore, yesterday called for a full enquiry into the banking system. He said the the taxpayer has a huge bill to pay for the banks and there needs to be a full public enquiry into what happened.
Government Chief Whip Pat Carey said yesterday that the hearings of an inquiry into the crisis could be held in private initially to gather evidence.
He said the Government is not excluding public hearings at a later stage and added that it is important the Dáil would ultimately discuss the collapse.