The leftist coalition that won the most seats in France’s National Assembly in surprise results has demanded the immediate right to form a government, even though no grouping won a majority of seats.

It is unprecedented in France’s modern history to have a fractured parliament. Sunday’s vote raised the risk of paralysis for the European Union’s second-largest economy.

The legislature is split between the New Popular Front leftist coalition, President Emmanuel Macron’s centrist allies and the far-right National Rally.

Mr Macron on Monday asked his prime minister, Gabriel Attal, to continue handling day-to-day affairs, despite Mr Attal’s offer of resignation, less than three weeks before the start of the Paris Olympics.

Mr Macron is leaving on Wednesday for a Nato summit in Washington.

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French President Emmanuel Macron (Mohammed Badra, Pool via AP)

The leftist coalition’s three main parties — the hard-left France Unbowed, the Socialists and the Greens — began negotiations to find a candidate for prime minister.

The coalition in a statement called on Mr Macron to “immediately turn to the New Popular Front” and allow it to form a government. It said the “prolonged retention” of Mr Attal could be seen as an attempt to erase the election results.

“We solemnly warn the president of the republic against any attempts to hijack the institutions,” the statement said, adding: “If the president continues to ignore the results it will amount to betrayal of our constitution and a coup against democracy, which we will strongly oppose.”

The leftist coalition includes France’s former Socialist president Francois Hollande, who has made an unexpected comeback on the political stage as one of the most prominent candidates in the elections, winning a seat in his home town.

He is seen as a key player but did not speak to journalists as he joined fellow members of the Socialist party.

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Former French president Francois Hollande (Michel Euler/AP)

The New Popular Front “is the leading Republican force in this country and it is therefore its responsibility to form a government … to implement the public policies expected by the French people,” Green lawmaker Cyrielle Chatelain said.

Talks within the leftist coalition are complicated by internal divisions now that the goal for its hurried formation in recent days — keeping the far right from power in France — has been achieved.

Some are pushing for a hard-left figure for prime minister, while others closer to the centre-left prefer a more consensual personality.

France’s prime minister is accountable to parliament and can be ousted through a no-confidence vote.

“France Unbowed lawmakers are going into the National Assembly not as an opposition force … but as a force that intends to govern the country,” hard-left lawmaker Mathilde Panot said.

The top negotiator for the Socialist party, Johanna Rolland, said the future prime minister will not be Jean-Luc Melenchon, the divisive hard-left founder of France Unbowed who has angered many moderates.

Mr Melenchon, who did not run in the legislative elections, joined the talks at the National Assembly.

Speaking on France 2 television, Ms Rolland suggested the leftist coalition could work with centre-left members of Mr Macron’s alliance.

Some were accepting the need to make deals and get along.

“In my view, the French people sent us a clear message. They did not want to give an absolute majority to any specific political bloc so they’re ordering us to listen to one another, work together and that’s what we need to do,” said Yael Braun-Pivet, a member of Mr Macron’s centrist alliance and former president of the National Assembly.

According to official results, all three main blocs fell far short of the 289 seats needed to control the 577-seat National Assembly, the more powerful of France’s two legislative chambers.

The results showed just over 180 seats for the New Popular Front, more than 160 for Macron’s centrist alliance and more than 140 for the far-right National Rally party of Marine Le Pen.

Mr Macron has three years remaining in his presidential term.