Ireland has warned there will be no Brexit withdrawal treaty and no transition agreement unless Britain comes up with acceptable wording as a “backstop” solution to the Irish border question in the event of no deal.

The Irish foreign minister, Simon Coveney, told reporters in Luxembourg that difficulties would arise as early as June if the wording was not agreed.

Asked whether the transition agreement would be at risk if there was no deal in place by June, he said: “It puts everything at risk. Michel Barnier [the EU chief negotiator] has been very clear there will be no withdrawal agreement if there is not a backstop relating to the Irish border consistent with paragraph 49 of the political agreement in December.

“The British government have committed to doing [backstop] that. If that is not in the withdrawal agreement, then there will be no withdrawal agreement and there will be no transitional deal either.”

The vexed question of how to retain an open border between Northern Ireland and the Republic is the subject of six weeks of side talks between officials from London and Brussels. They are three weeks in with a formal review due on Wednesday between Britain’s lead negotiator, Olly Robbins, and the EU’s deputy chief negotiator, Sabine Weyand.

Asked whether the UK was closer to agreeing wording that would mean full alignment in regulations north and south of the border, Coveney said: “Not at the moment”.

The UK and the EU agreed three options on Northern Ireland in the joint report on Brexit signed in December. Option A was that a solution would be found in the wider deal, option B was a bespoke arrangement and option C the backstop solution of full alignment of regulations on both sides of the border in the event of talks breaking down.

But when the EU translated option C into legal text, May said no prime minister could accept a draft that would involve Northern Ireland remaining in the customs union and the single market.

Many believe the latest talks have kicked the can down the road, and Coveney has warned that time is running out if Britain is to agree its final Brexit deal by October.

“If there is not substantial progress on the Irish border, the backstop, [which is] simply in line with what the British have committed to, then I think there will be difficulties in June,” he said in reference to the next summit of EU leaders scheduled to review Brexit talks.