Ireland will not make preparations for a hard border on the island, the Taoiseach said.
The Republic will begin planning at its ports and airports for the unlikely scenario of a no-deal Brexit, Leo Varadkar added.
The Irish premier said it was a possibility that the UK would "crash out" of the EU customs union and single market without an agreement with time was running out.
He attended a meeting of leaders at the European Council summit in Brussels.
Dutch Prime Minister Mark Rutte said the Irish border had to be the "first, second and third priority" in the Brexit negotiations and the UK needed a permanent border backstop plan.
The Taoiseach addressed the impact of a no-deal Brexit at the ports and airports.
He said: "Other countries are going to be doing it too, it is not just an issue for Ireland, it is as important an issue in Rotterdam or Calais or the ports of the Netherlands, Belgium or France.
"So we have to start making preparations for that, even though it is a very unlikely scenario, any responsible government has to make those preparations."
The future of the Irish land border is one of the most vexed issues still facing negotiators in Brussels ahead of next year's divorce.
The Irish premier reiterated that he was not preparing for any sort of physical border between Northern Ireland and the Republic and trusted the assurances of the UK and the EU that won't happen.
"However, if we have a no-deal Brexit, and that is unlikely but possible, then the UK will essentially crash out of the customs union and the single market, will not be able to trade freely any more with any part of the EU including access to a European market of 500 million people.
"That would require us to make preparations in our ports and airports for that kind of scenario and that is the kind of thing that we will be doing."
Mr Varadkar said the UK needed to soften some of its red lines.
"We as the 27 are willing to be more flexible. But in order to be more flexible the UK needs to soften some of its red lines.
"There are things we just cannot compromise on, the four freedoms and the single market have to go together.
"You cannot have one freedom or two freedoms or three-and-a-half freedoms because if we were ever to agree to that, the EU would start to break up, and that is something we cannot ever contemplate."
The 300-mile Irish land border is free-flowing and essentially invisible at present and the British Government has said it is seeking to ensure "frictionless" arrangements after the exit.
Northern Ireland Secretary Karen Bradley has said the Government's plan will be proposed next month.
A backstop option, agreed in principle between the EU and UK, has been interpreted by Europe to mean Northern Ireland will stay in the bloc's Customs Union if no other deal is reached.
The British Government is adamant it will not accept any proposal which draws a distinction between Northern Ireland and the rest of the UK.
A "Brexit breakfast" is scheduled for leaders on Friday morning.