Donald Tusk, the president of the European council, has told Theresa May that there will be no further Brexit negotiations after Downing Street announced its plan to return for new talks to the bewilderment of officials in Brussels.

As the prime minister told MPs that she was delaying the Commons vote on her Brexit deal and had sent her most senior Brexit adviser, Olly Robbins, to the European commission headquarters for fresh talks, Tusk dashed any hopes of a new EU offer.

Calling on EU leaders to up their no-deal preparations, Tusk said the 27 heads of state and government would not reopen the deal when they discuss Brexit at their summit starting in Thursday.

“We will not renegotiate the deal, including the backstop, but we are ready to discuss how to facilitate UK ratification”, Tusk tweeted. “As time is running out, we will also discuss our preparedness for a no-deal scenario.”

Presented with the tweet as she stood in the House of Commons justifying her delay to the meaningful vote, May declined to comment.

The European commission, led by Jean-Claude Juncker, had also insisted earlier in the day that there would be no further concessions to Britain despite the crisis in Westminster.

May makes Commons statement after calling off key Brexit vote – Politics live Read more

“Our position remains we will not renegotiate the deal that is on the table right now and that was endorsed by the EU council on 25 November, so that is very clear and as the president said himself, this is the deal and the only deal possible,” a spokesman said.

EU sources said Robbins had been sent to Brussels to secure an exchange of letters or side-declaration from the EU pledging that the backstop in the withdrawal agreement, which could keep the UK in an indefinite customs union, will never come into force and would be temporary.

Echoing Tusk’s comments, Ireland’s taoiseach, Leo Varadkar, who spoke to May on Sunday, said such a clarification of the EU’s intentions would be possible, but pointed to the lack of substance to such an offer.

Varadkar said it would not detract from the legal reality that the UK would fall into the backstop by default if another solution for avoiding a hard border on the island of Ireland was not realisable by the end of the transition period.

“We have already offered a lot of concessions along the way,” he said. “We ended up with the backstop with this withdrawal agreement because of all the red lines the UK laid down along the way.

“This is a withdrawal agreement which has the support of 28 member states. It’s not possible to open up any one aspect of this without opening up all aspects of the agreement.

“I have no difficulty with statements that clarify what’s in the withdrawal agreement [like Gibraltar], but no statement of clarification can contradict what’s in it.”

An EU diplomat involved in the negotiations said there was widespread confusion over the prime minister’s move: “The backstop is the backstop. What legal reassurances can you have [that] you would not use it?”

Others described Robbins’ return to Brussels as desperate, while senior EU sources suggested a clarification over their intentions would “be like dust” in the face of the legally binding 585-page treaty.

The bloc’s chief negotiator, Michel Barnier, has already said the EU has no intention of triggering the backstop but that it has to remain in place as an insurance.

The European parliament’s Brexit coordinator, Guy Verhofstadt, a former Belgian prime minister, expressed his frustration with May.

He tweeted: “I can’t follow anymore. After two years of negotiations, the Tory government wants to delay the vote. Just keep in mind that we will never let the Irish down. This delay will further aggravate the uncertainty for people & businesses. It’s time they make up their mind!”

Leaving a meeting in Brussels, the Dutch foreign minister, Stef Blok, said: “Of course we will look carefully at any proposal she might make. But we know how difficult it has been to reach agreement. So if there will be talks, it won’t be easy.”

Josep Borrell, Spain’s foreign minister, said of Britain’s MPs: “I think it is a good deal, I think it is the best deal and to approve this deal would be a good thing but for sure it’s up to them.”