The 92-year-old retired cleric was taken from his home in south Belfast earlier this week after suffering heart problems.
Last night, Cardinal Daly was still receiving emergency treatment at the Belfast City Hospital’s coronary care unit.
Yesterday Cardinal Brady asked Catholics to pray for Cardinal Daly, “that he may be given all the graces that he needs. While this is a sad time for all, we should be heartened and nourished by Cardinal Daly’s motto which is ‘Jesus Christ, yesterday and today’.”
This is the second time in a month that the 92-year-old former archbishop of Armagh has been treated in hospital.
Cardinal Daly was born in 1917 and ordained a priest in 1941.
He was appointed Bishop of Ardagh and Clonmacnoise in 1967 and installed as Archbishop of Armagh in 1990. A year later he was created Cardinal.
He retired in October 1996, when Cardinal Sean Brady took over the role.
Cardinal Daly is renowned for a being a prolific writer and has had published many philosophical papers.
He is also highly regarded for his work with Irish Bishops on the New Ireland Forum in the 1980s and leading a delegation on the Forum for Peace and Reconciliation in the 1990s, both of which were set up to explore ways of ending violence in the North.
He is known as a long-time critic of the IRA campaign.
Following the Downing Street declaration in 1993, he said any fair-minded person would agree the British government had made significant movement towards recognising the legitimacy of Irish republicanism and accepting the principle of self-determination for the people of Ireland.
He said rejecting the Downing Street declaration would mean republicans “would have nowhere to go, no political future, no place in the shaping of a future for Ireland, no hope of any access to political dialogue or political power-sharing”.