Irish banks have been guaranteed by the government
The Irish government has been asked to consider extending its emergency banking legislation to other institutions operating in Ireland.
Fine Gael leader Enda Kenny said the government had to ensure there was a level playing field.
Finance Minister Brian Lenihan has indicated he will consider applications from banks with a large high street retail presence in the Republic.
A statement said applications would be considered on a case by case basis.
Banks such as the Ulster and National Irish Bank, which are owned by companies outside the Irish Republic, are dismayed by the commercial advantage given to their competitors by the legislation.
The Credit Institutions Protection Bill 2008 is at its second stage in the Dail parliament as up to 28 amendments to its provisions are being debated.
The government's 400bn euro guarantee covers Allied Irish Bank, Bank of Ireland, Anglo Irish Bank, Irish Life & Permanent (which owns permanent tsb), Irish Nationwide Building Society and the Educational Building Society.
With the scheme also covering the institutions' branches in the UK, some opponents of the move say it will unfairly make the Irish banks more attractive than their British counterparts.
The British Bankers' Association said that Ireland's move had put British banks at a competitive disadvantage.
"The extent of the guarantee has clear consequences for firms competing to win retail deposits," a spokesperson said.