They had previously called for the Offaly TD to resign from cabinet.
The Irish Road Victims' Association says it's accepts an apology from the Agriculture Minister and will work with him going forward.
Its founder Donna Price says Minister Cowen contacted her to personally to apologise for drink-driving in 2016.
Earlier this week, the organisation called for the Laois/Offaly TD to resign from cabinet.
Ms. Price says she was shocked by his actions, but is drawing a line in the sand on the issue: