"Our people have clearly rejected the worst-case scenario," said the three-time presidential candidate of the France Unbowed (LFI) party.

Leftist parties including LFI, the Socialist Party, the Greens and the Communist Party joined forces last month to form the New Popular Front (NFP) after President Emmanuel Macron called snap polls.

Prime Minister Gabriel Attal "has to go... The New Popular Front is ready to govern", Melenchon said.

It is unclear who might be the alliance's top candidate to be prime minister, with Melenchon a divisive figure even among some supporters of his own party.

Within Melenchon's party, LFI lawmaker Clementine Autain called on the NFP alliance to gather on Monday to decide on a suitable candidate for prime minister.

The alliance, "in all its diversity", needed "to decide on a balance point to be able to govern", she said, adding neither former Socialist president Francois Hollande nor Melenchon would do.

The leader of the Socialist Party (PS) Olivier Faure urged "democracy" within the left-wing alliance so they could work together.

"To move forward together we need democracy within our ranks," he said.

"No outside remarks will come and impose themselves on us," he said in a thinly veiled criticism of Melenchon.

'Melenchon... cannot govern' 

Raphael Glucksmann, co-president of the smaller pro-European Place Publique party in the alliance, said everyone was going to have to "behave like adults".

In the projections, "we're ahead, but in a divided parliament... so people are going to have to behave like adults," he said.

"People are going to have to talk to each other."

Communist leader Fabien Roussel, who lost his seat in the first round, said the left would rise up to the task ahead.

"The French have asked us to succeed. And we accept that challenge," he said.

Marine Tondelier, the 37-year-old leader of the Greens, said it was too early to start suggesting the name of a prime minister.

But "we will rule," she said.

Macron made the gamble of calling the parliamentary polls three years early after the far right trounced his centrist allies in European elections.

Stephane Sejourne, the secretary-general of Macron's Renaissance party who has been foreign minister, won a seat in Sunday's polls.

It is "obvious... Melenchon and a certain number of his allies cannot govern France", he said.

"The lawmakers from the centrist bloc will ensure this in parliament."