The row has overshadowed the early days of Ireland’s new coalition Government, which was formed last month between leading parties Fianna Fail and Fine Gael, with the support of the Green Party. And it has also added to the existing tensions between Mr Martin’s Fianna Fail and former Taoiseach Leo Varadkar’s Fine Gael.
Mr Cowen is a brother of former Irish premier Brian Cowen and is part of a long-running Fianna Fail dynasty based in Co Offaly.
He has previously held frontbench spokesman roles on Environment and Local Government and Social Protection.
The married father-of-four and former auctioneer represents the electoral district of Laois-Offaly.
He had refused to make a second public statement about a drink driving ban imposed on him four years ago.
Addressing the Dáil in Dublin last night, Mr Martin said the police file relating to Mr Cowen’s drink-driving offence had raised issues that required more explanation.
He said it was untenable for members of Government to address these concerns in the Dáil while Mr Cowen was refusing to do so.
And he warned the issue had become damaging to the ongoing work of Government.
Mr Martin said: “This is a very sad day for Barry, his family and for me.
“He has been a very committed public representative, very diligent and very dedicated.
“Over the course of the last 10 days he has been the subject of significant criticism and condemnation for a road traffic offence that took place in 2016.
“He has been completely clear and unambiguous regarding his drink-driving offence.
“He gave a personal statement to this house on July 7 in which he talked about the stupidity of his actions, he accepted that what he did was absolutely wrong and he apologised to all members.”