He will not be undertaking any engagements in the near future.
In a statement yesterday the archdiocese said that his condition was improving.
"After a comfortable night the archbishop's condition is greatly improved and he is responding well to treatment. He has been advised that he will require a substantial period of convalescence and he will therefore not be undertaking any engagements in the immediate future. The archbishop is thankful for all the prayers and good wishes which he has received," the statement said.
The archbishop's hospitalisation casts doubt over whether he will be able to preside at the cathedral's Midnight Mass, which will be broadcast on Radio 4.