A DEAL on the border must be done by October, Taoiseach Leo Varadkar has said.
If no deal is agreed, a backstop option will mean Northern Ireland would continue to follow EU regulations after Brexit.
Unionists have opposed any solution which would create differences between Northern Ireland and the rest of the UK and Prime Minister Theresa May is reliant on DUP support in key Westminster votes.
Ahead of a meeting with European counterparts in Brussels Mr Varadkar said: "Everyone takes the view that we will have to have the withdrawal treaty agreed by October because it will have to be ratified by the British parliament and the European parliament, and potentially by some national parliaments. So October is the deadline.
"Would I like to have it done by June? Yes, absolutely. But I would rather have the right deal in October rather than any deal in June."
He envisaged a close trading relationship between the UK and the EU, "so close that many of measures in the backstop may become unnecessary".
The British Government is facing increased pressure to find a solution to the border, on which there has been little detailed agreement with the EU.
Avoiding a hard border is generally defined as one without frontier checks on goods and services but there has been no evidence of a technological solution for frictionless trade anywhere else in the world, a committee of MPs said.
The President of the European Parliament Antonio Tajani said yesterday: "The onus is now on the British Government to propose such a solution.
"But I want to make it clear once again that the European Parliament will not give its consent to a withdrawal agreement that does not incorporate solutions to rule out hard borders between the two parts of the island and which can be implemented immediately.
"We must heed the principle that 'nothing is agreed until everything is agreed', not least in order to ensure that the discussions on future relations are not hijacked by this delicate question."
Mr Varadkar reiterated his firm stance on the importance of the backstop arrangement if no other solution is found.
But he said that was not his preferred option and envisaged a "deep" free trade agreement between the UK and EU.
He added: "A customs union partnership between the UK and EU that would be so close to the customs union that it would not necessitate some of the elements that are in the backstop."
Meanwhile, eight EU leaders have signed a statement backing Liberal Democrat calls for the British public to have the final say on any Brexit deal.
The joint statement - backed by prime ministers of the Netherlands, Belgium, Denmark, Finland, Luxembourg, Slovenia, Estonia and the Czech Republic - was released after Sir Vince Cable travelled to Brussels for a meeting with fellow liberal leaders on the margins of the European Council.
Sir Vince - who is campaigning for a second referendum on the Brexit deal - said the statement showed that other EU states would "welcome an exit from Brexit with open arms".
