The outspoken host of BBC1's 'Newsnight' made his comments in an interview with the 'Radio Times' magazine.
He said: "Apologising for things that your great, great, great, great-grandfather or grandmother did seems to me a complete exercise in moral vacuousness."
Committee for the Commemoration of the Irish Famine Victims chairman Michael Blanch said Mr Paxman was in "denial" if he thought an apology was not appropriate.
"Saying sorry often starts the process of recovery and healing and while the Famine happened a long time ago it was right that a representative of the state which allowed it to happen apologises," said Mr Blanch.
"If Mr Paxman was making similar comments in certain European countries denying what happened during World War II he would be incarcerated," he added.
It read: "That one million people should have died in what was then part of the richest and most powerful nation in the world is something that still causes pain as we reflect on it today."