(AFP) - Almost two months after France's inconclusive legislative elections, impatience is growing with the reluctance of President Emmanuel Macron to name a new prime minister in an unprecedented standoff with opposition parties.

Never in the history of the Fifth Republic -- which began with constitutional reform in 1958 -- has France gone so long without a permanent government, leaving the previous administration led by Prime Minister Gabriel Attal in place as caretakers.

A left-wing coalition emerged from the election as the biggest political force but with nowhere near enough seats for an overall majority, while Macron's centrist faction and the far-right make up the two other major groups in the National Assembly.

To the fury of the New Popular Front (NFP) coalition, Macron earlier this week rejected their choice of economist and civil servant Lucie Castets, 37, to become premier, arguing a left-wing government would be a "threat to institutional stability".

Macron insisted during a Thursday visit to Serbia that he was making "every effort" to "achieve the best solution for the country".

"I will speak to the French people in due time and within the right framework," he said.

- 'Serious political crisis' -

Macron's task is to find a prime minister with whom he can work but who above all can find enough support in the National Assembly to escape swift ejection by a no-confidence motion.

Despite the lack of signs of progress in public, attention is crystallising on one possible "back to the future" option.

Former Socialist Party grandee Bernard Cazeneuve, 61, could return to the job of prime minister which he held for less than half a year under the presidency of Francois Hollande from 2016-2017.

He is better known for his much longer stint as interior minister under Hollande, which encompassed the radical Islamist attacks on Paris in November 2015.

But Cazeneuve receives far from whole-hearted support even on the left, where some in the Socialist Party (PS) regard him with suspicion for leaving when it first struck an alliance with hard-left France Unbowed (LFI) -- a party which in turn sees the ex-PM as too centrist.

Another option could be the Socialist mayor of the Paris suburb of Saint-Ouen, Karim Bouamrane, 51, who has said he would consider taking the job if asked. Bouamrane is widely admired for seeking to tackle inequality and insecurity in the low-income district.

The stalemate has ground on first through the Olympics and now the Paralympics, with Macron showing he is in no rush to resolve the situation.

"We are in the most serious political crisis in the history of the Fifth Republic," Jerome Jaffre, a political scientist at the Sciences Po university, told AFP.

France has been "without a majority, without a government for forty days," he said, marking the longest period of so-called caretaker rule since the end of World War II.

- 'Rubik's cube' -

Macron's move to block Castets even seeking to lead a government provoked immediate outrage from the left, with Green Party chief Marine Tondelier accusing the president of stealing the election outcome.

National coordinator for the hard-left France Unbowed (LFI), Manuel Bompard, said the decision was an "unacceptable anti-democratic coup", and LFI leader Jean-Luc Melanchon called for Macron's impeachment.

Some leftist leaders are urging for popular demonstrations on September 7, although this move has alarmed some Socialists and led to strains within the NFP.

France is in a "void with no precedents or clear rules about what should happen next," said Mujtaba Rahman, managing director for Europe at the Eurasia Group consultancy.

The president was "confronted with a parliamentary Rubik's cube without an obvious solution," said Rahman.

October 1 is the legal deadline by which a government must present a draft budget law for 2025.

The president has a constitutional duty to "ensure" the government functions, said public law professor Dominique Rousseau.

"He's not going to appoint a government that we know will be overthrown within 48 hours," he added.

For constitutional scholar Dominique Chagnollaud, Macron has backed himself into a corner, creating "unprecedented constitutional confusion".

The logical choice is to appoint a leader from the group that "came out on top," said Chagnollaud. "In most democracies, that's how it works. If that doesn't work, we try a second solution, and so on."

© Agence France-Presse