The move comes at a time when banks here were expected to cut rates, as the European Central Bank is due to start reducing its interest rates from next week.
The move by Bank of Ireland comes just days after fast-growing digital bank Revolut launched a savings product in the Irish market in a move seen to rasie the stakes for the three main banks.
There are hopes now that Revolut has sparked a price war on savings rates.
Revolut to put the squeeze on the banks with new savings product
The money app, which claims it has 2.7 million customers in this country, piled on the pressure, with savings rates of up to 3.49pc.
Now Bank of Ireland is to introduce a new two-year fixed-term deposit rate for personal and business customers of 3pc APR (annual equivalent rate)
And there will be a new one-year fixed-term deposit rate for personal and business customers of 2.50pc.
The new rates will be available from June 6.
The bank said there is will be no upward limit on funds that can be deposited or on funds that will attract interest, while up to 25pc of funds can still be withdrawn during the term.
Bank of Ireland director, retail Ireland, Susan Russell said: “Our new one and two-year fixed-term accounts offer better rates along with flexible features like being able to access some of your cash if needed and easy account opening in-branch or online.
“There is no requirement to open a current account and no fees or subscriptions to access these rates.”
Daragh Cassidy of price comparison site Bonkers.ie said: “These are competitive rates from Bank of Ireland.
He said that over the past few weeks, we have seen both N26 and Revolut launch new savings products for their customers in Ireland and this appears to be a clear response to that.”
Mr Cassidy said that although the new Bank of Ireland products are fixed rates, customers can withdraw up to 25pc of their money during the term which is feature that is not common in the Irish savings market.
He said Irish savers are collectively missing out on billions of euro in interest a year by not putting their money into the best yielding savings accounts.
Instead, they are leaving it in accounts that pay little to no interest. And this apathy is also helping the banks make record profits.
But with the ECB expected to start cutting interest rates from next week, now really is the time for savers to do something with their money before savings rates start to fall too, Mr Cassidy said.