The chairman of the Oireachtas Finance Committee, Ciaran Lynch, has said that the committee is best placed to conduct the inquiry into the 2008 bank bailout, which was announced by the Taoiseach yesterday.
Meanwhile, Independent TD Shane Ross has said it is "frankly ridiculous" to proceed with the inquiry without considering Anglo Irish Bank.
He said the bank's footprints were all over the period leading up to the bank guarantee.
Taoiseach Enda Kenny told the Dáil yesterday that the Government has approved plans for an Oireachtas banking inquiry.
The inquiry will look at the bank guarantee and events leading up to it, the role of banks and auditors and the role of State institutions.
Mr Kenny said the Government will ensure that the probe is well resourced and has the full co-operation of State institutions.
He said it would also have regard for impending criminal trials.
The Taoiseach said the timing of the inquiry is a matter for the Oireachtas, saying there will not be an instruction from Government and it will be decided by TDs.
The Committee on Procedures and Privileges will have a role in establishing the inquiry, he added.