The DUP has held out an olive branch to Theresa May over Brexit, offering to work with her to get changes to the deal with the EU to get it passed by MPs.

Officials have been locked in talks with the EU over Christmas in an effort to get legally enforceable changes to the so-called Irish border backstop which has sparked fierce opposition to the deal from the DUP and Tory Brexiteers.

DUP Westminster leader Nigel Dodds held talks with Chief Whip Julian Smith on Wednesday morning with the prime minister under pressure to secure the necessary changes before MPs start debating the deal next week.

The support of the Northern Irish party is seen as key in avoiding a crushing defeat for the deal in a Commons vote the following week, with one Tory former cabinet minister telling HuffPost UK “she will have to persuade the DUP” by “really moving the dial” on the backstop.

But despite EU leaders rubbishing the DUP’s demand for the withdrawal agreement to be reopened last month, Dodds made clear the party would not back down.

After the meeting with the chief whip, Dodds said: “The DUP has been consistent in these negotiations. 

“The withdrawal agreement would undermine the constitutional and economic integrity of the United Kingdom.  

“The Prime Minister has committed to secure changes.  

“We will be holding her to her word.  

“We want to work with the Government in the coming days to ensure the United Kingdom leaves the EU with a good deal.”

In a tweet which was then deleted, Dodds’ DUP colleague Sammy Wilson struck a harsher tone, warning May against pursuing “meaningless reassurances” rather than changes to the legal text.

But Dodds’ offer to work with the PM marks a softening of the DUP’s relations with the government since its furious reaction to the deal struck with Brussels in November threatened to kill off the confidence and supply deal that props up her minority administration.

Meanwhile, Tory opponents of the deal said they had seen little over the Christmas break to change their minds, despite suggestions time away from Westminster could dampen a rebellion thought to be around 100-strong.

The ex-cabinet minister, who did not want to be named, told HuffPost UK: “People have consumed their mince pies and looked lugubriously over the fence at 2019 and seen little to change their views over Christmas.”

But a senior backbencher with good knowledge of colleagues’ views said a legally-binding “codicil”, or addendum, to the deal could get the DUP onside and subsequently unlock the support of “a number of Conservatives” and potentially Labour MPs in Leave seats.

That would give the deal a “reasonable” chance of passing, they said.

Earlier, Foreign Secretary Jeremy Hunt confirmed the government was continuing to try to change details of the backstop within the withdrawal agreement, in a clear sign it is committed to getting DUP support for the deal.

He told BBC Radio 4’s Today programme: “Theresa May has been very clear this isn’t just about words but about text which has legal force.

“She has also been very straightforward about this – the EU has agreed the backstop is temporary and that’s a word they have agreed.

“So what we’re saying, very simply, is we’re not asking for anything new but we are asking you to define what temporary means so we can have confidence we’re not going to be trapped in the customs union for ever against the wishes of the British people.”