RBS said it had offered 6.20 euros a share for First Active, valuing the business at 887 million euros ($1bn; �600m).

The offer, which still requires the backing of First Active's shareholders, represents a 33% premium on the Irish bank's closing share price on Friday.

First Active, a retail bank and mortgage lender, will complement RBS' existing Irish subsidiary, the Ulster Bank.

RBS said the two businesses, which between them serve about 1.3 million personal and business customers, would create "a highly effective challenger to the larger competitors in the Irish banking market."

Synergies

The bank aims to boost its revenues in Ireland by selling more mortgage products to Ulster Bank customers, and offering a "broader range" of banking products to First Active customers.

It also plans to cut costs by combining the two banks' technology and processing activities.

However, First Active and Ulster Bank will continue to operate under their own brands.

RBS chief executive Fred Goodwin predicted a rosy future for the bank's Irish operations.

"The combined business will focus on customer service, income growth and efficiency," he said.

"I believe that it is capable of becoming the best bank in Ireland under each of these measures."