Jean-Claude Juncker has suggested that the UK is drifting towards another Brexit extension in October as he criticised MPs for prioritising the prime minister’s removal over finding agreement on a Brexit deal.

With May appearing on the brink of resignation, the European commission president spoke of his admiration for her resilience and his disdain for the attempts to remove her.

“What I don’t like in the British debate is it seems more important to replace the prime minister than to find an agreement among themselves,” Juncker said in an interview with CNN. “This is a woman who knows how to do things but she is unable to succeed in doing things. I like her very much; she is a tough person.”

Junker told CNN that he was “fed up” with the ongoing impasse but suggested that Brussels was resigned to a further request to extend the UK’s membership this autumn.

The UK has until 31 October to agree a deal, leave without an agreement or seek a further extension of the article 50 negotiating period.

Juncker said: “I hope they will agree among themselves, and they will leave [the EU] by the end of October ... I think it’s their patriotic duty to get an agreement.

“I am getting fed up because we are [just] waiting for the next extension.”

The commission president added that it was not about the “identity of the next prime minister; it’s about the withdrawal agreement”.

The commission president’s backing is unlikely to dissuade many Conservative cabinet ministers and MPs from seeking to force the prime minister out of office.

Following the resignation of the leader of the House of Commons, Andrea Leadsom, on Wednesday, May’s hold on power looked weaker than ever before.

With the EU refusing to renegotiate the withdrawal agreement, Juncker suggested that there was little to be gained in changing the country’s leadership.

One of the stated reasons for Leadsom’s resignation was May’s offer to facilitate a vote in the Commons on a potential second referendum.

Juncker struck a sceptical note when asked whether he agreed with Donald Tusk, his counterpart in the European council, that the UK should hold a second Brexit vote.

He said: “I would like to say yes to a second referendum, but the result might not be any different. We are observers in a British stadium – it’s up for them to decide.”

As leader of the House of Commons, Leadsom had been expected to give details on Thursday of the withdrawal agreement bill. But she claimed in her resignation letter that she could not sign up to facilitating another referendum.

In her response, May denied that this was her intention. “I do not agree with you that the deal which we have negotiated with the European Union means that the United Kingdom will not become a sovereign country,” May wrote.

May said that any bill was likely to attract an amendment seeking to bring a second referendum about. “That is why at cabinet yesterday we agreed to bring the bill forward and allow those MPs who want another referendum to put their case,” the prime minister said.