Taoiseach Leo Varadkar has denied the extension offered by the EU to the UK is an example of the rolling cliff-edge Brexit scenario.
Asked whether the EU was now in the midst of a rolling exit, he replied: "It's not. There won't be further extensions.
"We've set out now what the timeline is and in many ways the European Union has taken control of the timeline which in the past had been set by the UK."
Mr Varadkar made the comments at the end of the summit of EU leaders in Brussels. He said the choices were now "very obvious".
"It's this agreement; no deal; or the parliament taking indicative votes for a much closer long-term relationship with the EU which would allow the joint political declaration aspect of the withdrawal package to be amended," he said.
"I don't see any other choices."
Irish leader Varadkar speaking bluntly about differences within EU27 and solidarity pic.twitter.com/vHlPqOWJAf— Lili Bayer (@liliebayer) March 22, 2019
He added: "I hope the Withdrawal Agreement will be ratified by the House of Commons. If it isn't I imagine they'll go onto indicative votes and that may point the way to a closer long-term relationship."
The Taoiseach said the view of Theresa May is that it would be a "farce" for the UK to participate in the European Parliament elections.
"(Mrs May) gave some indication in that from her point of view, there is no desire whatsoever to take part in the European elections.
I think she feels, and most British politicians feel, it would be a farce for the UK to participate in the elections if it were to leave and that's mainly the reason why the date of April 12 was chosen, because that is when they have to trigger the European elections and so they need to know they're definitely going by then, or if they're going to stay or there's going to be a long extension well then the European elections will have to happen in the UK.
Mr Varadkar said Mrs May is confident she can win her upcoming vote.
"Prime Minister May feels there is a pathway to victory and getting a majority in the House of Commons, and I hope she can achieve that," he said.
"I wouldn't be in a better position than she is to access the parliamentary arithmetic that exists in the UK and it's a political matter for the British Parliament."
Meanwhile, DUP deputy leader Nigel Dodds has said Theresa May failed to secure changes to her Brexit deal - including the Northern Ireland backstop - at the summit in Brussels.
"The Prime Minister missed an opportunity at the EU Council to put forward proposals which could have improved the prospects of an acceptable Withdrawal Agreement and help unite the country," he said.
"That failure is all the more disappointing and inexcusable given the clear divisions and arguments which became evident amongst EU member states when faced with outcomes they don't like."
He added: "Nothing has changed as far as the Withdrawal Agreement is concerned. We will not accept any deal which poses a long-term risk to the constitutional and economic integrity of the United Kingdom."