His comments came after Catholic bishops issued a statement denouncing the 'Protection of Life during Pregnancy Bill' as a "morally unacceptable change" in law.
Dr Brady indicated the church may challenge a bill that would force church-run hospitals to provide abortions against their own code of ethics and morals.
He said the bill does not give institutions – such as Catholic hospitals – the option to refuse performing abortions on conscientious grounds.
This, he claims, could be seen as a denial of fundamental religious freedoms.
He also said the proposed legislation has "potentially menacing implications" for all Catholic institutions, including hospitals .
The bishops also expressed concern that the proposed law would "impose a duty on Catholic hospitals to provide abortions".
"This would be totally unacceptable and has serious implications for the existing legal and constitutional arrangements that respect the legitimate autonomy and religious ethos of faith-based institutions," they wrote.
The bill, if passed, would also "pose serious difficulties for the conscientious beliefs of many citizens," they added.
Morally
In the statement, issued just days after the Government published the bill, the Catholic hierarchy said it maintains its belief that deliberately depriving a human being of life is always morally wrong.
"The heads of the Protection of Life during Pregnancy Bill 2013 published by the Government would, if approved, make the direct and intentional killing of unborn children lawful in Ireland," the bishops said.
"The bill as outlined represents a dramatic and morally unacceptable change to Irish law and is unnecessary to ensure that women receive the life-saving treatment they need during pregnancy."
The proposed law would, if enacted, legislate for the 1992 X case judgment from the Supreme Court which ruled that abortion can be legally performed if there is a real and substantial risk to the mother's life under certain circumstances.
They include the mother's threat of suicide as well as both emergency and non-emergency medical conditions.
Tanaiste Eamon Gilmore reacted to the statement saying he respected the right of the bishops to their views.
However,
he said Ireland was a democratic country and laws are made by those
elected by the people, adding that the failure of legislators to address
the issue for the past 21 years was now being addressed.