Minister for Finance Brian Lenihan has signalled that he is not willing to intervene in the decision by Permanent TSB to raise its variable interest rates by 0.5%.
In a statement, Mr Lenihan said that while he was disappointed, the increase reflected commercial market realities.
Earlier, SIPTU General President Jack O'Connor said the Government should withdraw the State guarantee from any banks that raise interest rates.
The country's largest mortgage lender will increase rates on standard variable loans on Monday.
Speaking on RTÉ's Morning Ireland, Jack O'Connor said it was immoral for the bank to raise rates at this time.
The move would damage consumer confidence and reduce consumer demand, thus jeopardising even more jobs in the economy, he added.
Also speaking on Morning Ireland, Fine Gael leader Enda Kenny called on Minister for Finance Brian Lenihan to intervene directly to stop rate rises.
Permanent TSB, which is owned by Irish Life & Permanent, has been under pressure due to the credit crunch.
It is losing money in its tracker loans and trying to make up the shortfall by increasing rates elsewhere.
People on standard variable rates will see rates increase from 2.69% to 3.19% from Monday.
More than 50,000 borrowers will be affected.
The move will mean monthly repayments on a €300,000 mortgage will increase by €70 a month.
Most of its customers who took out mortgages over the past five years are on tracker loans and will not be affected by the move.
Bank of Ireland, Ulster Bank, Halifax Bank of Scotland and KBC Homeloans say they have no immediate plans to follow suit but will be watching the move closely.
It is understood that the Department of Finance would generally be kept informed of such moves.