The husband and wife who lived in Athlone are said to have been in their 50's – with an adult daughter.
It brings to three the number of Irish people when a gunman opened fire at a beach in Sousse.
Lorna Carty from Co Meath was the first Irish victim to be identified from the 38 dead.
At least 15 British tourists were killed, along with Belgians, Germans and French and several people are injured.
Tributes are being paid to Laurence and Martina Hayes – local TD Denis Naughten says the family is very well known Athlone and south Roscommon:
