A Government spokesman said last night that Mr Ahern was proceeding with the visit despite Government advice to the public to cut out unnecessary cross-channel travel, because he saw it as an important trip.
"It is important for the Welsh Assembly for us to go," the spokesman said.
Mr Ahern is visiting on foot of a longstanding invitation to address the Welsh national assembly today on Wales' national day, St David's Day. He is the first overseas head of government to be asked to address the Welsh Assembly.
However, Mr Ahern has dropped two functions from his programme, as they would have been attended by large numbers of people and would have constituted an "unnecessary risk".
Mr Ahern will travel to Cardiff this morning from London, were he had talks at Downing Street last night with the British Prime Minister, Mr Blair. He is due to hold talks with the Welsh First Minister, Mr Rhodri Morgan, before addressing the National Assembly at noon.
This afternoon he will travel to Newport, just outside Cardiff, where he will deliver an address entitled "Europe: The Irish Viewpoint" to an international forum on Wales, Europe and the world.