Theresa May will present MPs with new “clearer language” on the nature of the backstop agreement, the foreign secretary, Jeremy Hunt, has claimed, as the prime minister held telephone talks with the German chancellor and other EU leaders.

Talks with the heads of EU countries and the DUP have been quietly going on during the festive period, Whitehall sources have confirmed, as May prepares to face mutinous MPs when she returns to the Commons having promised legally binding concessions.

A German government source confirmed Angela Merkel had spoken with May on Christmas Eve and again on Wednesday, as part of a series of calls the British prime minister has made to EU leaders over the festive period as she attempts to guide her Brexit deal through the Commons.

Downing Street remained silent on the details of the calls and has not revealed the list of EU leaders, but a No 10 source said May had more calls lined up this week. Berlin said it could not comment on the private conversations.

Cabinet ministers have privately urged the prime minister to prioritise securing an agreement which would bring the DUP, which is propping up her government, back onboard.

The Northern Irish party has vowed to vote down the deal unless legally-binding changes are made. Private talks have been held with DUP MPs since May pulled the parliamentary vote she had intended to hold in December after it became clear she would face a massive defeat.

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Sammy Wilson, the DUP’s Brexit spokesman, said in a now-deleted tweet that he was in London for a government meeting, believed to include the chief whip. “Off to London for meetings with senior ministers. We aren’t interested in meaningless assurances,” he tweeted. “The legal text is what counts and the prime minister has promised changes. Let’s see!”

MPs are to restart the debate on May’s withdrawal agreement on their return to parliament on Monday.

Ahead of their return, the Brexit secretary, Steve Barclay, will convene a meeting of junior ministers on Thursday to discuss updates to the preparations for a no-deal exit.

May has said she is seeking further legal reassurances from EU leaders about the permanence of the backstop agreement, which would keep the whole UK in a single customs territory with the EU until both sides agreed on an alternative solution to prevent a hard border between Northern Ireland and the Irish Republic.

Hunt, who is in Singapore, said May would eventually get her Brexit deal approved. “I think that she will find a way to get this deal through parliament and I know that is what the British people would want,” he told an audience Q&A.

The foreign secretary said a no-deal outcome could cause disruption for a prolonged period, adding: “That is not something any government should wish on its people.”

Speaking later to the BBC, he reiterated May’s desire to find a solution that would have 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,” said Hunt.

“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.”

Hunt, who has attempted to burnish his pro-Brexit credentials in recent weeks, said there was a need to unite leavers and remainers but that should not be via a second referendum, adding it would be a “devastating blow to democracy”.

Instead, he said the deal had to be “a friendly separation where we have the closest possible trade relationship, the closest possible diplomatic relationship with our European friends and neighbours, because I think that is the biggest fear of the remainers”.

He added: “We need to find a way of making sure that the Brexit that 48% are afraid of isn’t the Brexit that we end up with and I am confident we can succeed.”

Hunt had initially floated the idea of a second referendum, which he now opposes, days after the 2016 result, saying the deal needed “democratic endorsement in some form”.

The Labour MP Virendra Sharma, a supporter of the pro-remain Best for Britain campaign, said: “While he seems to have decided it’s no longer advantageous for his personal leadership prospects to back a people’s vote, the arguments for putting this decision back in the hands of the people have grown, as the consequences of the political uncertainty come home to roost and our parliament remains in deadlock.”