Donald Tusk has accused MPs of showing a lack of respect for the British prime minister as the EU turned its fire on the Commons over its failure to back the Brexit deal.

As he closed a summit in Brussels, the European council president took aim at treatment meted out to Theresa May, who faced a challenge to her leadership on the eve of the leaders’ meeting.

“We have treated Prime Minister May with the greatest respect, all of us, and we really appreciate the efforts by the prime minister to ratify our common agreement,” Tusk said. “My impression is that in fact we have treated prime minister May with a much greater empathy and respect than some MPs, for sure.”

Earlier in the day, May had confronted the European commission president, Jean-Claude Juncker, accusing him of calling her “nebulous” in a press conference.

Juncker said the row had been a misunderstanding, adding that he had been describing the “overall state of the debate in Britain”.

“I was following the debate in the house and I can’t see where the British parliament is heading at and that’s why I was saying it’s nebulous,” he said.

The French president, Emmanuel Macron, said the Brexit deal was now “in the hands of the British parliament” and called on MPs to take a clear position on whether to accept or reject it. “This agreement, I believe, is truly good for both parties and it is the only one possible,” he said.

May faces an uphill battle to persuade MPs that the Northern Ireland backstop contained in the withdrawal agreement would not trap the UK in a permanent customs union.

She has pinned her hopes on a last-ditch effort to persuade the European Union to work with her in devising a legal guarantee, known as a “joint interpretative instrument” that would put a duty on both sides to try to get out of the Irish backstop within 12 months of it coming into force.

Secret negotiations between May’s Brexit adviser, Olly Robbins, and senior EU officials had teed up the leaders on Thursday evening to issue a statement assuring the UK that the backstop would only ever be temporary.

They were also due to offer future assurances on hearing from the prime minister but that pledge was taken out of the statement at a late dinner, on the demand of a large number of member states, including Ireland, France, Denmark, Belgium and Spain.

On Friday, the EU’s leaders avoided questions from reporters about the possibility of answering May’s calls for a legal instrument to convince her MPs back home of both sides’ intentions on the backstop.

Asked three times whether the UK could get further concessions or legally binding assurances that go beyond the current agreement, the German chancellor, Angela Merkel, declined to suggest another offer would be forthcoming.

“The 27 member states have given assurances, they are contained in the conclusions of yesterday evening,” she told reporters. “So that is our position, that is what we have put on the table and now we expect Great Britain to respond.”

EU leaders think the summit communique already has legal weight. It is “not just a sheet of paper, but these are conclusions of the 27 member states”, Merkel said.

The Irish taoiseach, Leo Varadkar, said the EU could not put a date by which the UK would exit the backstop. He said: “Obviously we want to be as helpful as possible … but there are limitations to that.”

Tusk said he would not negotiate with May over a legal guarantee, but that he would be available to her over the Christmas period. “I have no mandate to organise any further negotiations”, he said.

“We have to exclude any kind of reopening our negotiations on the withdrawal agreement. But of course we will stay here in Brussels, and I am always at prime minister Theresa May’s disposal.”