The European commission president, Jean-Claude Juncker, has told Boris Johnson that the EU27 will not give in to his demand to renegotiate the Brexit withdrawal agreement.

On Thursday in his first telephone call with Johnson as prime minister, Juncker called the existing deal “the best and only agreement possible”.

Johnson has insisted the agreement to leave the EU and arrangements regarding the Irish border are not good enough and should be renegotiated.

Juncker said the EU would analyse any ideas put forward by the UK provided they were compatible with the withdrawal agreement, his spokeswoman Mina Andreeva tweeted in a readout of the phone call.

Juncker declined to speak to Johnson on Wednesday when it emerged that the earliest opening for a conversation was past midnight in Brussels.

Michel Barnier, the EU’s chief Brexit negotiater, said on Thursday that Johnson’s “combative” rhetoric since becoming prime minister was an attempt to crack the EU’s unity, and he rejected the new UK government’s central demand over the Irish backstop.

In a note sent to diplomats in Brussels, Barnier counselled the EU27 to stick to its principles in the face of Johnson’s no-deal threats.

Johnson had insisted the UK would leave on 31 October “no ifs or buts”, in his speech on the steps of Downing Street on Wednesday. In his first address to the Commons as prime minister on Thursday he said his government would not accept any agreement containing the “undemocratic” Irish backstop.

Barnier said in his note that he would not engage in talks with the British government over binning the backstop, an arrangement designed to avoid a hard border on the island of Ireland.

“PM Johnson has stated that if an agreement is to be reached it goes by way of eliminating the backstop. This is of course unacceptable and not within the mandate of the European council,” Barnier wrote.

“While he has declared that he will only engage with the EU on this basis, we are on our side ready to work constructively, within our own mandate. We will analyse any UK idea on withdrawal issues that are compatible with the existing [withdrawal agreement], and we are of course ready to rework the political declaration, in line with the EUCO guidelines.

“But as suggested by his rather combative speech, we have to be ready for a situation where he gives priority to the planning for no deal, partly to heap pressure on the unity of the EU27. No-deal will never be the EU’s choice, but we all have to be ready for all scenarios.”

The backstop contained in the withdrawal agreement agreed by Theresa May would keep Northern Ireland under large swathes of single market regulations and the whole of the UK in a shared customs territory “unless and until” an alternative arrangement can be found to avoid the need for border checks on the island of Ireland.

Some Conservative MPs are opposed to the arrangement in the belief that it will trap the UK in a close economic relationship with the EU that would prevent the British government from developing an independent trade policy.

But Barnier noted in his email to diplomats the rejection by many MPs of any attempt by Johnson to take the UK out of the EU without a deal.

In comments that signal the growing belief in Brussels that the UK is heading towards a general election, Barnier wrote: “I note also the many strong reactions to the speech in the House of Commons. In this context we must follow carefully the further political and economic reactions and developments in the UK following this speech.

“In any case, what remains essential on our side is to remain calm, stick to our principles and guidelines and show solidarity and unity of the 27. I remain available throughout the summer for talks with the UK and of course with you should you have questions.”

Barnier ended his missive by promising to send an analysis of any British proposals to the member states on receiving them.

Luisa Porritt, the deputy leader of Liberal Democrat MEPs, said: “It is welcome that Michel Barnier, the EU27’s chief negotiator, acknowledges the inherent weakness of the Conservatives’ grip on power here in the UK. Boris Johnson’s government is as unstable as Theresa May’s was. Beyond the bluster there is no good reason to believe he can implement Brexit. He must break the deadlock in parliament by putting the deal back to the people.”