Former Taoiseach Bertie Ahern has called for direct negotiations between London and Dublin on relations after Brexit.
The Mr Ahern said the internationally binding Good Friday Agreement peace deal allows bilateral talks between the countries on issues other than trade.
At present, Ireland will negotiate with Britain only as a member of the EU27 bloc.
Mr Ahern said European Union leaders - including Guy Verhofstadt, Michel Barnier and Jean-Claude Juncker - do not disagree on the right for separate Anglo-Irish talks.
In the Seanad he said the Good Friday Agreement specifically allows for it.
"It is an international agreement, and we have every right to bilaterally negotiate - not the trade issues, we accept that is the European Union - but on several of the other issues, to be able to negotiate with the British," he said.
"For the life of me, I don't understand why or accept the argument that we are precluded on those issues."
Mr Ahern added: "I know Guy Verhofstadt, I know Michel Barnier, I know Jean-Claude Juncker. I've dealt with these guys for 20 years - they don't have a different view.
"The strength of our argument on non-trade issues is that the Good Friday Agreement allows it and says it."
Mr Ahern, who played a key role in the 1998 peace accord, said there are many concerns "in relation to the island of Ireland and particularly on Northern Ireland" that should be dealt with on a London/Dublin basis.
He also predicted any Brexit deal would take longer than two years to complete - up to 10 years for a trade agreement - and agreed that any necessary EU treaty change would have to be passed by a referendum in Ireland under its constitution.
This could effectively hand Ireland a veto over a British deal with the EU.
Speaking before a special Brexit committee, he predicted free movement would continue across the Irish border, including for EU nationals, after Britain pulls out of the bloc.
But he warned the free movement of goods and services is a "big problem".
Mr Ahern said he agreed with Lord King, former head of the Bank of England, that the tax and trade border could by moved to the Irish Sea.
The forrmer taoiseach also warned now is not the time for a border poll on Irish unity.
A "sectarian headcount" in Northern Ireland is the last thing that is needed amid the fall-out of Brexit, he told senators.
"The last thing I want out of Brexit, the very last thing, is anyone (going) on about border polls," he said.
"The only time we should have a border poll in my view, and I will argue this for the rest of my life, is when we are in a situation where nationalists and republicans and a sizeable amount of unionists and loyalists are in consent.
"To have a sectarian headcount now is the last thing we need."
But Mr Ahern said the provision for Irish reunification, enshrined in the Good Friday Agreement, should be stitched into any Brexit deal between the UK and the EU.
Sinn Féin, who made gains in the recent Stormont elections, has insisted there is an urgent need for a reunification referendum after the UK vote to pull out of the EU.
The majority of voters in Northern Ireland backed remaining within the EU - 56% to 44%.
But the Democratic Unionist Party has accused Sinn Féin of creating further uncertainty and division in calling for a border poll.