The Democratic Left leader suggested the Taoiseach invite the British Prime Minister to address the Dail. Mr Proinsias De Rossa said this would be a mark of appreciation to Mr Blair "for the excellent co-operation between the two governments in putting the Belfast Agreement together with the parties in Northern Ireland".
A whole new era of co-operation had been opened up between Ireland Britain, he added.
Mr Ahern replied: "I have noted what you said about inviting Prime Minister Tony Blair. I hope that he will be here shortly to discuss the Northern agreement and other matters with me at government level. Anything else I would consider over a longer term."
Mr De Rossa's suggestion was supported by the Fine Gael leader, Mr John Bruton, who said it was ironic that the German Chancellor, the French president, three presidents of the United States, and many others had addressed the Dail, but not the State's nearest neighbour.
"Now that we have normalised state-to-state relationships with Britain, surely it is about time we invited the British Prime Minister, the same as we invite other prime ministers, and stop maintaining a constitutional fiction that our relationship with Britain is different to our relationship with other states," he added.
On the Northern assembly elections, the Taoiseach said he would encourage all those voting to think carefully before they voted and do so on the basis of electing people who would contribute constructively to it.
Mr De Rossa said the Taoiseach should urge a voluntary moratorium by all marchers on all sides for the summer so as to give the people of Northern Ireland a chance to heal the wounds of the last 30 years.
Mr Bruton said the parades issue could cause problems in the North over the summer, and he believed a solution could be found if the Orange Order agreed to meet all resident groups and in return they agreed to allow parades of a non-confrontational kind to pass.
Mr Ahern said progress could be made on the issue if there was compromise. "If we could move both sides on this issue, we could make some progress," he added.
Meanwhile, the Fianna Fail TD, Mr Ben Briscoe, has said Mr Blair should be invited to speak to the Dail as soon as possible and his speech should be televised live.
In a letter to the Taoiseach, the Dublin South Central deputy said such a move would "symbolise the new mature and closer relationship between these two islands" and "would be welcomed throughout the island".