President Emmanuel Macron faced an uphill battle Tuesday seeking fresh talks over a new government in France, with the political left refusing to take part after he rejected their candidate for prime minister.

More than seven weeks after an inconclusive parliamentary election which cost his allies their relative majority, Macron has still not named a new prime minister to take over from the current caretaker administration.

Left-wing coalition the New Popular Front (NFP) emerged from the vote as the largest bloc, but well short of an absolute majority.

In the 577-seat National Assembly, the NFP has over 190 seats, followed by Macron's centrist alliance at around 160 and Marine Le Pen's far-right National Rally at 140.

The NFP have nevertheless demanded that the president pick their candidate Lucie Castets, a 37-year-old economist with a history of left-wing activism.

But late Monday, Macron ruled out naming a left-wing government, saying it would be a "threat to institutional stability".

Instead, he called on "all political leaders to rise to the occasion by demonstrating a spirit of responsibility".

Macron's office said that it would be pointless to name a NFP government as it would immediately be rejected by a no-confidence vote in parliament.

The president called on the socialists, ecologists and communists in the leftist alliance to "cooperate with other political forces", in an apparent attempt to lure the more moderate members of the coalition away from LFI.

But on Tuesday, Socialist party boss Oliver Faure refused Macron's overture, saying he would "not be an accomplice to a parody of democracy".

Socialist deputies would back a no-confidence motion against any government that was not put forward by the NFP, he said, accusing the president of seeking to "prolong Macronism" despite losing the National Assembly election.

'Annoyed, to say the least'

"French people will start to get annoyed, to say the least," Faure warned, saying he himself would take part in street protests, after Communist party leader Fabien Roussel -- who also rejected new talks with Macron -- called for a "grand popular mobilisation".

"The left is being robbed of this election," said Green Party chief Marine Tondelier.

"We won't be part of this mess anymore," she said.

Castets accused Macron of seeking to be "president, prime minister and party leader all at the same time", adding that this was "not respectful of French voters or of democracy".

LFI founder Jean-Luc Melenchon even threatened to start impeachment proceedings against Macron.

The far-right National Rally (RN) has not been invited to Tuesday's talks.

Meanwhile Francois Bayrou, a highly-respected veteran centrist, chided the president for getting bogged down in negotiations with political parties which he said was "the wrong method".

Instead, he said, Macron should seek out a candidate with experience of high office.

"There are people who have held the office of president," he said, "others who had high government positions" or "who have represented political movements and currents".

Macron's office has not given any indication about the president's timetable for naming a prime minister -- but the clock is running to October 1, the legal deadline by which a government must present a draft budget law for 2025.

Macron is also scheduled to open the Paris Paralympic Games on Wednesday, and is expected in Serbia on Thursday for an official visit.