Ian Paisley jnr said his family wanted to thank all those who had sent messages of support since his 85-year-old father was admitted to the Ulster Hospital near Belfast.
“He is doing very well,” said Mr Paisley, who succeeded the former Democratic Unionist leader as North Antrim MP.
“We are incredibly grateful to the many hundreds of people who have contacted us and indicated that they are praying for us and praying for my father.
“I am glad that he is making progress; we continue to need distance and space.”
Mr Paisley, 85, was rushed to the Ulster Hospital at Dundonald at the start of the month suffering from apparent heart failure. At one stage he was in intensive care.
Known as Lord Bannside since he was made a peer in 2010, he fell ill just ten days after preaching his final sermon as a church minister.