Permanent TSB has become the latest to reduce its fixed rates, after Ulster and KBC also reduced their mortgage costs.
Experts said AIB and Bank of Ireland would now have to respond.
Permanent TSB has cut its three-year fixed rate for first-time buyers from 3.3pc to 3.15pc.
The lender also cut its five-year fixed rate from 3.4pc to 3.25pc.
One of the rates will be as low as 2.9pc. But this only applies to those borrowing more than €250,000.
The bank has also cut fixed rates for borrowers with a loan-to-value ratio of between 60pc and 80pc by 0.15pc.
But Fianna Fáil has criticised Permanent TSB for not passing on the fixed-mortgage rate cuts to its existing customers.
"While I welcome all interest rate cuts, Permanent TSB has once again discriminated against its own customers by not extending interest rate cuts to them," said finance spokesman Michael McGrath.
He said new mortgage customers of the bank can avail of fixed rates as low as 2.95pc, but the best fixed rate available to an existing customer is 4.2pc.
Asked about existing customers, a spokesman for Permanent TSB said it reviewed its rates on an ongoing basis.
"Existing customers, in particular those on standard variable rates, should consider moving to a managed variable rate which offers considerable reductions depending on the loan to value of the mortgage," he said.
Permanent TSB has also extended its 2pc cash-back offer until September. This means new borrowers receive 2pc of the value of the mortgage they take out in cash upfront, as well as 2pc of the monthly payments back in cash every month.
Mark Whelan, of price comparison site Bonkers.ie, said Permanent TSB's new fixed rates would be among the most competitive in the Irish market.
He said that a first-time buyer borrowing €270,000 at Permanent TSB's previous rate of 3.3pc over 30 years will have a monthly repayment of €1,182.
But a buyer borrowing €270,000 at the bank's new rate of 3.15pc will have a monthly repayment of €1,160. This will mean savings of €22 a month, or €264 a year.
"Permanent TSB's rate cuts are good news for Irish borrowers, who have been paying much more than their European counterparts for too long.
"It is the third mortgage rate reduction we've seen in three weeks, which means we are in the midst of a new mortgage-rate war.
"All eyes will now be on AIB and Bank of Ireland to see how they respond," Mr Whelan said.
Banking analysts said the rate cuts were modest in size but indicate heightened competition among borrowers over the past year.
Since last autumn, all five of the main high street banks have announced large cuts to their mortgage rates.
Analysts at Davy Stockbrokers, Diarmaid Sheridan and Stephen Lyons, predicted more rate reductions.
"The reductions in mortgage rates are in line with our expectations, where we continue to expect decreases in new mortgage lending rates across our forecast horizon (to 2020)," they wrote in a note to investors.
Permanent TSB group commercial director Mark Coan said the new rates would offer real value to customers and peace of mind as speculation grows on possible interest rate rises later this year or early next year.