French President Emmanuel Macron on Tuesday was holding talks with the opposition on ending the deadlock sparked by his failure to secure a majority in parliamentary elections, after rejecting an offer by the prime minister to resign. 

Macron was to host far-right leader Marine Le Pen and other political party chiefs for rare talks at the Elysee as he seeks solutions to an unprecedented situation that risks plunging his second term into crisis two months after it began.

The spectre of political paralysis and the breakthrough performance by the far-right under Le Pen has also raised questions over Macron's leadership in Europe as he seeks to keep a prime role in dealing with the Russian invasion of Ukraine. 

The Elysee said French Prime Minister Elisabeth Borne, blamed by some analysts for heading a lacklustre campaign, had offered her resignation to Macron but the head of state turned it down.

Macron believes the government needs to "stay on task and act" and the president will now seek "constructive solutions" to the political deadlock in talks with opposition parties, said a presidential official, who asked not to be named. 

Macron started Tuesday's flurry of discussions by talking with Christian Jacob, the head of the traditional right-wing the Republicans (LR), a party on the decline in recent months but which now may be courted by the president to give him a majority. 

Socialist Party leader Olivier Faure and Communist Party boss Fabien Roussel -- members of the NUPES left-wing alliance -- will also meet Macron.

And in a rare encounter, Macron will at 17:30 Paris time (1530 GMT) host Le Pen, his rival in presidential elections and leader of the far-right National Rally (RN).

No question of pact

The options available to Macron range from seeking to form a new coalition alliance, passing legislation based on ad hoc agreements, or even calling new elections.

One option would be an alliance with the Republicans, which has 61 MPs. 

But Jacob after the talks appeared to close the door on such a solution. "I told the president there was no question of entering into what could be seen as betrayal of our voters."

"We will stay in opposition.... there is no question of thinking about some kind of pact," he said, while vowing the party would not block the work of institutions.

Macron had hoped to mark his second term with an ambitious programme of tax cuts, welfare reform and raising the retirement age. All that is now in question.

"What can he (Macron) do now?" said the headline in the Le Parisien daily. "Macron in an impasse, NUPES already divided," added Le Figaro. 

While Macron's Ensemble (Together) coalition remains the largest party after Sunday's National Assembly elections, it fell dozens of seats short of keeping the absolute majority it has enjoyed for the last five years.

Macron's Together alliance won 245 seats, well short of the 289 needed for an overall majority, in a low-turnout vote that resulted in an abstention rate of 53.77 percent.

The election saw NUPES become the main opposition force along with its allies on 137 seats, according to interior ministry figures.

But it appears unlikely the coalition of Socialists, Communists, Greens and the hard-left France Unbowed will be able to retain common cause in the legislature.

Listen to voters

Jean-Luc Melenchon, the France Unbowed chief who orchestrated the NUPES alliance, proposed Monday to make NUPES a permanent left-wing bloc but the offer was immediately rejected by the three other NUPES parties.

In a snub to the president, Melenchon is believed to be sending deputies to Elysee talks with Macron on Wednesday rather than going himself.

Meanwhile the far-right under Le Pen posted the best legislative performance in its history, becoming the strongest single opposition party with 89 seats, up from eight in the outgoing chamber.

Le Pen said changing the prime minister "would not change much", urging Macron to "listen to what the French voters said".

Even if Borne will stay in her post for now, a cabinet shake-up is on the horizon.

Macron's health and environment ministers were beaten and by tradition will have to resign, as did the parliament speaker and the head of Macron's parliament group.