Taoiseach Leo Varadkar has said he made it clear to British Labour leader Jeremy Corbyn that the Brexit Withdrawal Agreement is "closed" and will not re-open unless there is a "fundamental change" in the red lines from the next prime minister.
He said one such decision would be to stay in the customs union or the single market.
Mr Varadkar also said the chances of an extension of Britain's departure date from the EU are "slim" and there is a "hardening view" across the EU that there cannot be a rolling extension.
He was responding to questions at an Oireachtas Committee about Mr Corbyn's suggestion during a visit to Dublin, that he would re-negotiate the UK's exit deal if he became prime minister.
"I very much emphasised to him that the Withdrawal Agreement is closed," Mr Varadkar said in response to questions from the chair of his party's Brexit committee, Senator Neale Richmond.
"Any change to the political declaration is possible, but the Withdrawal Agreement is closed and the only way that that could ever change would be if there was a fundamental change in red lines from the next UK prime minister or the next UK government.
"For example, a decision to stay in the customs union or to stay in the single market, and I think that was well understood by him," he said.
"We also talked about how hard it would be to secure any extension beyond 31 October.
"There is a hardening view across the EU that we cannot continue to have rolling extensions, and while there could potentially be a further extension if there was an election to allow that election to happen or if there was a referendum, I don't think it is viable to believe that there would be sufficient support or unanimous support around the European Council for a further extension while the UK tries to figure it out or for another set of indicative votes."
"So I very much imparted that message as politely as a I could that the chances of a further extension are pretty slim, and the Withdrawal Agreement including the Irish protocol and the backstop is closed from our point of view."
Mr Corbyn earlier said that he and his party held what he called "a very good discussion" on Brexit with Mr Varadkar at Government Buildings today.
Speaking to RTÉ's Prime Time, Mr Corbyn said he did not want the UK to "crash out without a deal".
He said he wanted to make sure that the Good Friday Agreement is fully upheld in all of its forms.
Mr Corbyn said it was the Labour Party's intention to ensure that happened and he said that is why he had visited Dublin at the invitation of Mr Varadkar.
Mr Corbyn added that the "crucial" issue is ensuring an open border on the island of Ireland.
He said that contenders for the leadership of the Conservative Party might be happy to see the UK "crash out" of the European Union without a deal, but he was not.
Asked how Mr Varadkar reacted to the possibility of reopening negotiations with the EU on Brexit, Mr Corbyn said the Taoiseach "responded positively", despite pointing to the obvious reality that the makeup of the new European Commission was not yet known.
The two men held discussions lasting 90 minutes, according to a Government statement.
Additional reporting Fran McNulty