The Rev Ian Paisley was in intensive care on Monday evening after suffering acute cardiac problems.
The former Northern Ireland First Minister was admitted to the Ulster Hospital in Dundonald on the eastern outskirts of Belfast.
A statement on behalf of his wife, Baroness Paisley, said: "She requests that the family's privacy be respected at this difficult time."
Paisley, 85, was rushed to hospital on Sunday, 10 days after preaching his final sermon as a minister. He is a former moderator and founding member of the Free Presbyterian Church and was MP for North Antrim for almost 40 years.
Paisley, now known as Lord Bannside, was succeeded in North Antrim by his son Ian Jnr.
Party colleagues were briefed in a meeting at Parliament Buildings, Stormont, and prayers were said. One member said they were given no details about how he became ill or his condition. "We were just told he was unwell and in hospital. That was all."
It is understood Paisley has been on medication for several years for an enlarged heart, possibly since 2004. According to one source tonight the illness could be linked to heart failure, not a heart attack.
There had been concerns several years ago about Paisley's health when he lost weight and looked gaunt.
But he made a good recovery from heart problems and while his voice was showing signs of obvious weakness, some people who were at his farewell sermon at the Martyrs Memorial Church in Belfast on January 27 remarked on how well he appeared for his age.
One member of the congregation said: "I have rarely seen him in better form. Steady on his feet, it was typical Paisley cracking the odd joke with a jibe. He may have looked 85, but he was in fine form, really good."
After withdrawing from church and public life he was planning to write his autobiography.
Paisley, once a fierce opponent of sharing government powers with nationalists and republicans in Northern Ireland, was elected first minister in May 2007 with Martin McGuinness, a former IRA leader in Londonderry, as Deputy First Minister.
It was a remarkable partnership, the two men becoming firm professional and personal friends who were later nicknamed the "Chuckle Brothers".
Paisley's five children - twin sons Ian Jnr and Kyle, an ordained minister as well, and three daughters, Rhonda, Sharon and Cherith - were among the 3,000 people for his final address.
He said: "I am exceedingly happy that I've had the privilege of being the preacher here for 65 years, and that's a long time.
"We have seen a miraculous work done, and we have seen a great change in our city in many ways. We've seen a change spiritually by people having respect for the bible."
He underwent tests for an undisclosed illness in summer 2004 and afterwards admitted he had "walked in death's shadow".
Some years later he had a pacemaker fitted after feeling unwell at the House of Lords.
Paisley was a fierce critic of the 1998 Good Friday Agreement which led to the formation of the first power-sharing administration at Stormont since 1974.
But in the aftermath of the signing of another political arrangement, which became known as the St Andrews Agreement of 2006, he underwent an astonishing political transformation which culminated with him going into power with Sinn Fein a year later.
It was a deal which would have been unimaginable at the height of the IRA terrorist campaign, but this was a much different Ian Paisley from the firebrand preacher who spent decades on the margins of political power, damming the Catholic Church, and who was once thrown out of the European Parliament for denouncing Pope John Paul II as the antichrist.
He stood down as first minister in May 2008 with his long-time deputy party leader Peter Robinson taking over around the same time as he was made a life peer in Gordon Brown's Dissolution Honours List. He was MP for North Antrim from June 1970 until May 2010.