French President Emmanuel Macron has said he will name a new prime minister “in the coming days”, after Michel Barnier resigned following a no-confidence vote in parliament.

In a 10-minute address to the nation on Thursday, he rejected opposition pressure to stand down, vowing to stay in his post “fully, until the end of the mandate” in 2027.

Macron was holding talks on Friday with leaders of the Socialists, who said they were ready for a compromise in forming a government as part of a short-term deal.

The Socialists joined colleagues on the left and far right in voting to remove Michel Barnier on Wednesday, only three months after he was appointed by Macron.

The president thanked Barnier for his dedication during his brief term as prime minister, and accused MPs of collaborating in an “anti-republican front” to bring down the government.

The vote was the first time a French government had been voted down by parliament in more than 60 years, a move Macron labelled “unprecedented”.

In France, it is the president who chooses the prime minister who then runs the government. But the prime minister must answer to parliament and Barnier lasted only three months before he was ousted in a no-confidence vote.

Finding someone who will not be immediately rejected by parliament could be difficult for Macron, whose decision in June to call snap elections led to a deadlocked parliament.

The National Assembly is now split into three big voting blocs – the left, centre and far right. If Macron’s next choice of prime minister is to last, it is thought at least part of the left bloc will need to be persuaded to join the next government.

The president was due to hold talks with several political leaders on Friday, having told the French people he would “appoint in the coming days a prime minister who will form a government of general interest”.

He held talks with centrists in the “Macron camp”, before meeting Socialist leaders, in the hope of persuading them to split from the broader left bloc, the New Popular Front. He will also talk to the right-wing Republicans.

Socialist leader Olivier Faure said ahead of the talks that he was open to discussion and “compromises on every issue” towards forming a government based on a “fixed term contract”. But he made clear he had little desire to “ensure the continuity of Macronism”.

No new parliamentary elections can be held until July 2025, which might explain Faure’s remarks on being open to a limited term for the next government.

Responding to Macron’s speech on Thursday, Marine Le Pen, leader of the far-right National Rally (RN), posted social media: “A little reminder to President Macron, who is supposed to be the guarantor of the Constitution: censure is not anti-republican, it is provided for in the Constitution of our Fifth Republic.”

The no-confidence vote that toppled Barnier’s leadership had been tabled by both the New Popular Front (NFP) left-wing alliance, and Le Pen’s RN.

They united to censure the government after the former Brexit negotiator used special powers to force through his budget without a vote.

A total of 331 MPs voted in support of the motion against Barnier, far more than the 288 required for it to pass.

Barnier resigned on Thursday, and the budget was automatically withdrawn. He will remain in office on a caretaker basis with his ministers until a new government is appointed. Macron’s role is unaffected.

Macron has been heavily criticised for deciding to call snap elections, creating a deadlock in parliament and an escalating political crisis.

He admitted in his address that his decision “was not understood”: “Many have blamed me for it and, I know, many continue to blame me. It’s a fact and it’s my responsibility.”

Addressing voters directly, he said some of his political opponents had chosen “chaos over responsibility” and that they were not thinking “about you, the voters”, suggesting their focus was on the next presidential elections.

Macron gave no indication of who the next prime minister would be, but said their immediate focus would be the budget for 2025.

Speculation has been swirling over who could be named, with potential candidates including Defence Minister Sébastien Lecornu, Interior Minister Bruno Retailleau, and centrist former presidential candidate François Bayrou.

Before Macron chose Barnier as prime minister, he asked his predecessor Gabriel Attal to stay on as caretaker for two months after the summer elections.

It seems highly unlikely that the next government can be in place before Saturday, when world leaders including US President-elect Donald Trump are due to attend the opening ceremony of the rebuilt Notre-Dame Cathedral in Paris.

The building was devastated by fire in April 2019, and its reconstruction little more than five years later has drawn worldwide praise.

Macron said the rebuilding of the ravaged cathedral, plus France’s successful hosting of the 2024 Olympics, were “proof that we can do great things”.

“We can do the impossible,” he said. “The world admires us for that.”