DUNDALK, Ireland (Reuters) - The EU’s Brexit negotiator expressed confidence on Monday that a solution for the Irish border can be achieved if rapid progress is made by June, but said a real risk remained of Britain leaving the bloc without an overall deal.

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Northern Ireland will be Britain’s only land frontier with the European Union after Brexit. Both sides say they are committed to keeping the border with the Irish Republic open, but finding a practical solution has proved elusive so far.

The EU and Dublin insist the Brexit treaty must lock in a backstop arrangement in case a future trade pact does not remove the need for border controls. London signed up for this last month but disagrees with the EU’s means of achieving it..

“We need to ... agree rapidly by June on the scope of all island customs and regulations - the safety and controls that we need to respect the single market,” negotiator Michel Barnier said, referring to an EU leaders’ meeting in June that he called a “stepping stone” towards reaching a full agreement in October.

“I am confident that together with unity of the EU27 and a constructive attitude on both sides, we will be able to agree the right solution,” he told a news conference in the Irish border town of Dundalk. However, he added: “There is a real risk and we have to be prepared for any options, including no deal.”

Under the EU proposal, if all other attempts to avoid a hard border fail, Northern Ireland would form a “common regulatory area” with Ireland and 26 other EU states, in effect keeping the British province in a customs union with the EU.

Britain, which is still debating its own Brexit strategy, says an EU-UK free-trade deal to be sealed by 2021 can solve the border issue, and Prime Minister Theresa May has rejected the EU proposal as a threat to the constitutional integrity of the UK.

“The backstop we put in the draft treaty is not there to change the UK red lines, it is there because of the UK red lines,” Barnier said.

“We are ready to work with any new proposal from the UK on the condition there will be no border between Ireland and Northern Ireland and the condition that the UK respects the integrity of the single market and customs union.”

Barnier was speaking at a Brexit conference organized by the Irish government alongside Prime Minister Leo Varadkar and Foreign Minister Simon Coveney.

Coveney said Dublin and Brussels agreed that they would not accept a situation in which everything is agreed except the Irish border, “where there is a pressure created to kick it on to the next stage”.

Barnier will travel across the border into Northern Ireland later on Monday.