The Democratic Unionist Party has told Theresa May not to “roll over” to the EU, heaping further pressure on the prime minister after her Brussels failure.

Arlene Foster – the leader of the party propping up the Tories in power – blamed Ms May personally for the setback, saying: “This is a difficulty of the prime minister’s own making.”

She said: “The prime minister has promised to get legally binding changes.

“The reaction by the EU is unsurprising. They are doing what they always do. The key question is whether the prime minister will stand up to them or whether she will roll over as has happened previously.”

The comments came after Ms May’s Brexit strategy was dealt a devastating blow after late-night talks at an EU summit in the Belgian capital ended in acrimony.

EU leaders scrapped proposed written commitments, designed to help her pass her deal through parliament, in frustration at the prime minister’s inability to set out clearly what she wanted.

The 27 heads of state and government opted to delete lines from their council conclusions, which would have said the EU “stands ready to examine whether any further assurance can be provided”.

Worryingly for Ms May, Ms Foster’s outburst follows the prime minister’s pledge – in a crisis meeting with Tory MPs – to rebuild battered relations with the Northern Irish party.

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The DUP is under pressure to vote with Labour in a vote of no confidence in the government, although it has said it will only do so if the deal is passed – which looks increasingly unlikely.

In her statement, Ms Foster added: “This is a difficulty of the prime minister’s own making. A deal was signed off which the prime minister should have known would not gain the support of Parliament.

“If the prime minister had listened to our warnings and stood by her public commitments, we would not be in this situation.”

Labour’s Keir Starmer said the overnight events in Brussels proved the prime minister was “obviously not” going to get the changes which were the reason for shelving the meaningful vote.

“She needs to put that vote back to parliament next week and let us vote on it,” he told Sky News.

“It’s unacceptable for this vote to be put off until January. We know the answer as to whether there are going to be any changes – and it is no.”

Leo Varadkar, Irish premier, emphasised that the EU was united on the need for the Irish border border backstop in the withdrawal agreement.

In Brussels for the second day of the European Council meeting, the Taoiseach said he was “very satisfied” with the summit conclusions on Brexit which made clear the withdrawal agreement was not “up for renegotiation”.