Update 9.37pm: Taoiseach Leo Varadkar met British Prime Minister Theresa May before the evening session of EU leaders in Brussels.
They spoke about Brexit, Northern Ireland, and Russia.
Caught up with British PM Theresa May this evening at @EUCouncil to talk Brexit, Northern Ireland, Russia, and also briefly rugby. She committed again to December agreement. Detailed discussions start next week on EU/UK future relationship with focus on Ireland pic.twitter.com/b5nYx7ohjF— Leo Varadkar (@LeoVaradkar) March 22, 2018
Mrs May reassured the Taoiseach of her commitment to the December Brexit blueprint.
They both looked forward to the negotiations next week at official level in Brussels on the border and will discuss Northern Ireland again after Easter.
The Taoiseach also expressed solidarity and support following the chemical attack in Salisbury.
Mrs May congratulated Ireland on winning rugby's Six Nations Grand Slam.
Earlier, 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."
Update 5.50pm: Better the right border deal in October than any deal in June, says Taoiseach
The outcome of Brexit will be a test for Ireland's membership of the EU, Taoiseach Leo Varadkar has said, as he again vowed there would be no new border in the North.
EU leaders will return to the thorny issue of Brexit today and are expected to agree to a transition deal for Britain.
But in surprise remarks, Mr Varadkar said that Ireland could be willing to wait until October before getting a solution on the so-called 'backstop' promise of a frictionless border in the North.
This follows a rejection of the backstop terms by British Prime Minister Theresa May, who ruled out accepting suggestions the North could remain in the EU customs union without any solution.
Nonetheless, Britain agreed earlier this week to put the backstop in the Brexit withdrawal deal, also saying it favours an alternative solution, including through technical means.
Asked by reporters yesterday when a clear deal or backstop might be agreed on the North, Mr Varadkar said it quite possibly could be as late as October.
“I think certainly by October. 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.”
Fianna Fáil warned during the week that the issue of the North had been kicked down the road and now faced being left behind in talks.
Speaking at an EU summit in Brussels, Mr Varadkar said agreement on the Brexit transition period up until the end of 2020 meant “really nothing will change until 2021 and that's very important when it comes to jobs and to business and when it comes to farming”.