Theresa May has warned she could walk away from the Brexit talks (Jack Taylor/PA)

DUP deputy leader Nigel Dodds has rejected claims that a row between the party and Prime Minister Theresa May is halting Brexit progress.

The Sun has reported that the DUP has rejected a plan by Mrs May to allow different rules for goods in Northern Ireland than the rest of the United Kingdom following Brexit to allow the Irish border to remain open.

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The paper claimed that DUP leaders had rejected the move as they felt it would split up the United Kingdom.

I was born on the Irish border. I want to see a sensible exit from the EU. The referendum result must be implemented. The Conservative & Labour parties reject a border in the Irish Sea. Time for Brussels to respect the constitutional & economic integrity of UK. https://t.co/3mdsaetfY3 — Arlene Foster #WeâllMeetAgain (@DUPleader) September 22, 2018

Irish Foreign Minister Simon Coveney also criticised the DUP saying that they should not be allowed to veto the proposed Brexit backstop deal.

The backstop would allow Northern Ireland to remain in the EU customs union if a Brexit deal cannot be reached.

The Tanaiste said that Brexit had become an "orange and green" issue in Northern Ireland.

"Parties in Northern Ireland have been put under real pressure mainly driven by fear," Mr Coveney told RTE's Marian Finucane programme.

"Unionists are fearful that a solution on this issue could result in barriers between Northern Ireland and the UK.

"Nationalists are fearful that they could see border infrastructure between where they live and where they regard as their country."

Mr Coveney said that there would be no agreement without a border solution.

"There will be no withdrawal treaty between the UK and EU if there isn't a legally operable text on the Irish backstop guaranteeing no physical infrastructure," the Foreign Minister said.

"We will never sign a treaty that doesn't ensure the commitments given to Ireland aren't followed through,"

Sinn Fein President Mary Lou McDonald echoed Mr Coveney's comments saying that "the DUP cannot veto the vote of the people of the north to remain as part of the EU".

The Dublin Central TD said it was time for the DUP and the UK government to "get real".

“They do not represent the views of the majority of people nor the interests of the economy," she said.

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“The DUP cannot veto the vote of the people in the north to remain.

“There will be no withdrawal agreement without a backdrop that protects the interests of all Ireland.”

However Mr Dodds said that the claims the DUP were interfering in Brexit negotiations were not true.

In a Tweet on Friday the North Belfast MP wrote "no rows with us".

"As PM said NO British PM could agree to EU demands to break up the UK."

In a speech on Friday Mrs May said the EU "did not respect" that Northern Ireland would remain part of the UK after Brexit after they rejected her Chequers plan.

She reiterated there would never be a border in the Irish Sea.

Mrs May demanded the EU come up with new proposals to break the current "impasse".

"The EU should be clear: I will not overturn the result of the referendum. Nor will I break up my country," Mrs May said.

"We need serious engagement on resolving the two big problems in the negotiations. We stand ready."

European Council president Donald Tusk said he believed that a deal could still be reached.

“While understanding the logic of the negotiations, I remain convinced that a compromise, good for all, is still possible. I say these words as a close friend of the UK and a true admirer of PM May,” he said.

Belfast Telegraph