Mr McDowell admitted that “very serious mistakes” were made by prison authorities in relation to the murder of Mr Douch.
Earlier this week, Gary’s mother, Margaret Rafter, called on Mr McDowell to resign and said she was considering taking legal action.
Yesterday, the minister said: “In relation to her rights, she is entitled to take, as a statutory dependant of Gary Douch’s, a legal action against the State if there has been a breach of his personal and constitutional rights or a breach of the State’s duty to him.”
He said the murder of her 21-year-old son was “an horrific event” that should not have happened.
“I have established, what I hope to be, a thorough investigation into the circumstances which led to an horrific killing.
“As far as I am concerned all the indications are that very serious mistakes were made in the manner in which it was dealt with and I am determined that the truth will be established and, secondly, that this will never happen to anybody else.”
Gary Douch, from Darndale, north Dublin, was beaten and strangled to death in a shocking attack while confined in an overcrowded cell in Mountjoy Jail on August 2 last.
He had earlier pleaded with prison bosses for protection.