National Irish Bank (NIB) is to apply to be included under the Government's bank guarantee scheme.
In a statement this morning Andrew Healy, chief executive of National Irish Bank said the bank had also brought its concerns about the scheme to the attention of the Government.
He said the guarantee could "distort competition and create an uneven playing field".
"The scheme in its current form excludes some banks which are an integral part of the Irish economy and commercial life, providing investment, employment and a vital high street presence for consumers and businesses."
Mr Healy said the scheme in its current form excludes some banks and could lead to confusion on the part of bank customers.
"It is therefore important that foreign-owned banks, with obvious commitment to Irish jobs, consumers and businesses, should not be discriminated against," he said.
National Irish Bank was bought by Danske Bank Group three years ago. The end of the first half of this year NIB had a loan book of over €10 billion and deposits of €3.2 billion.
Bank of Scotland (Ireland)/Halifax which is owned by UK bank Lloyds TSB-HBOS has formally applied for inclusion today and Ulster Bank said in a statement this afternoon that it has lodged an application and was "confident that our application will be successful".
Belgian-owned IIB has expressed concerns about being excluded from the guarantee.
