Taoiseach Leo Varadkar will warn British Prime Minister Boris Johnson that Ireland won't accept "some sort of halfway house" alternative to the backstop to avoid a hard border.
Mr Varadkar also responded to comments from European Commission President Jean-Claude Juncker that border checks will be an inevitable consequence of a no-deal Brexit.
He said the UK will be to blame if there is a return to some form of border checks in the event of a crash-out scenario.
And he insisted that Ireland won't cave on the need for the backstop or realistic alternatives while saying: "we will work until the very last moment to avoid no deal, but not at any cost.”
The Taoiseach is to meet Mr Johnson tomorrow on the sidelines of a UN summit in New York.
Mr Varadkar said it will be another opportunity for the pair "to compare notes, see if there's more common ground, [and] see if we can make more progress."
"Our bottom line is that we need a legally binding assurance that there won't be a hard border between North and South, that the all island economy will continue to operate, that North-South cooperation will be able to continue.
"We can't accept some sort of halfway house."
Proposals put forward by the British government last week on alternatives to the backstop have effectively been ruled out by the EU as not achieving its main aims.
In a Sky News interview broadcast at the weekend Mr Juncker bluntly confirmed that Ireland will have to implement border checks on the EU's behalf in the case of a no-deal Brexit while insisting Britain would be to blame. He also made remarks on the need to ensure there will be no hard or physical border with Northern Ireland.
The Irish government has been in talks with the EU on how to avoid this but has yet to outline to farmers and businesses whose goods cross the border how this will be achieved.
Mr Varadkar said today: “It is the case that in the event of no deal that checks will be necessary and the government has been saying that for many months now. "
He said there would be checks at ports and airports, "checks at business level, and also some checks near the border".
Mr Varadkar added: “If that happens, that will happen as a consequence of the United Kingdom deciding to leave without a deal.
"It won't be a decision that we've made, and it certainly won't be something that we sign up to or agree to anyway.”
Mr Varadkar argued that businesses and farmers "know a lot already" about what will happen if there's a no-deal Brexit.
He said: "They know what's going to happen in terms of customs declarations, they know what the tariff rates are going to be in the event of no-deal.
"They know that there will be lots of checks at the ports and airports and indeed the infrastructure is there now to do that."
Mr Varadkar added: "In relation to the arrangements near the border, I understand, of course, business and agriculture want to know what will happen in that scenario.
"But that hasn't been agreed between us and the European Commission.
"Once we know, we will inform people, but also we will give people a decent lead in time so that they'll have time to prepare."
The Taoiseach also responded to claims in the British media that Ireland will cave on the backstop as the October 31 Brexit deadline looms.
“One thing I do know about Brexit for the last two or three years, and there are some people in Britain...who took the view that sooner or later, the French, the Germans, the big countries would gang up on Ireland and that’s never happened.
“And there are also some people who may believe that at the last minute that Ireland would somehow fold or give up our position. That's not going to happen."
He outlined Ireland's position that the government is willing to examine alternative arrangements that achieve the same objectives to the backstop.
"If the United Kingdom can come up with alternative arrangements that meet those objectives, that are legally binding, well, we're willing to accept that and examine those," he said.
"But so far anything that they’ve come up with falls very far short of that."
Mr Varadkar has met European Council President Donald Tusk for around 45 minutes in New York today to take stock of the latest Brexit developments.
A government spokesperson said both men agreed they want Brexit deal.
They added: “The Taoiseach and President Tusk agreed that the EU side has not seen proposals from the UK that achieve the objectives of the backstop.
“They also agreed that time is very short if there is to be a positive outcome at the Europe Council [summit in October].”
British opposition Labour leader Jeremy Corbyn said yesterday his party would guide him on how to campaign in a second Brexit referendum, pledging to offer voters a choice between staying in the European Union and a "credible" deal.