PARIS, July 8 (Reuters) - The French left said it wanted to run the government but conceded on Monday that talks would be tough and take time, after Sunday's election thwarted the far right's quest for power but delivered a hung parliament.

Many of France's allies breathed a sigh of relief after Marine Le Pen's National Rally (RN) failed to win the snap election called by President Emmanuel Macron.

But with the leftist New Popular Front (NFP) alliance, hastily assembled before the election, unexpectedly coming first but far from an absolute majority, the election heralded a period of volatility and possible gridlock.

"It's not going to be simple, no, it's not going to be easy, and no, it's not going to be comfortable," said Green party leader Marine Tondelier. "It's going to take a bit of time."

Possibilities include the left forming a minority government - which would be at the mercy of a no confidence vote from rivals unless they reach deals - and the cobbling together of an unwieldy coalition of parties with almost no common ground.

"We'll need some time," NFP lawmaker Pouria Amirshahi told Reuters as newly elected lawmakers arrived in parliament to pick up their badges and settle in, adding that any option was complex.

The NFP has no single leader and, with an estimated 182 MPs, is far short of the 289 threshold needed for an absolute majority. No other group has a majority either. Macron's centrists came second and the RN third, leaving parliament split in three groups.

"The President of the Republic must call on us to run the government, to respect the outcome of the election," Manuel Bompard, of the hard left France Unbowed said before a meeting with the Socialists, Greens and Communists to decide on what strategy the NFP would take.

For Le Pen's RN, the result was a disappointment as opinion polls had for weeks projected it would win, RN lawmaker Laurent Jacobelli told Reuters, even if they increased their number of MPs by more than 50 to 143.

RN leader Jordan Bardella acknowledged that the party had made mistakes, including on the choice of some of its candidates, but assured that Sunday's ballot had sown the seeds for future victory for the far right.

Meanwhile, Prime Minister Gabriel Attal, a centrist and ally of Macron, tendered his resignation but Macron asked him to stay on for now "in order to ensure the country's stability," the president's office said.

Photo from Reuters