MINISTER FOR Health Mary Harney said she thought bank customers would benefit from the interest rate cut.
"There is good competition in the banking sector for depositors and for mortgage holders, and I expect the reduction will be passed on to the customers of banks.
"Two banks have already indicated that, and I am certainly hopeful the others will do so."
Fine Gael leader Enda Kenny said they did not want a situation where Irish banks were profiteering on the backs of taxpayers.
"This affects tens of thousands of householders," he said.
Labour leader Eamon Gilmore said it was the first time they had seen major international regulation and control of banking.
"The mortgage holder, the business that has a loan from a bank and the customers of banks should benefit from that," he said.
"It would be unthinkable for the banks not to pass on that reduction in interest rates to their customers."
He said the Government should direct the banks in the Republic to do so, given that the relationship between the Government and the banking system was entirely different from what it was.
Sinn Féin Dáil leader Caoimhghín Ó Caoláin said the Government should also insist that the local authorities pass on the reduction to those dependent on local authority loans.