EVRY, France (Reuters) - French Prime Minister Manuel Valls declared on Monday that he would seek the Socialist Party’s nomination for next year’s presidential election and said he was quitting the government to focus on campaigning.

Slideshow ( 3 images )

Although opinion polls bill Valls as the favorite for the Socialists’ ticket, they also forecast that neither he nor any other left-wing candidate will win the election, rather that conservative candidate Francois Fillon will beat far-right National Front leader Marine Le Pen in a run-off.

“We’re told the left does not stand a chance, but nothing’s set in stone,” Valls said to applause from supporters in his fiefdom of Evry, the gritty southern suburb of Paris where he was mayor for over a decade.

“I want us to lead the left to victory!” the 54-year-old said, urging his much-divided camp to unite.

The path was cleared for Valls to enter the race last week when deeply unpopular President Francois Hollande announced he would be the first leader since France’s Fifth Republic was created in 1958 not to seek a second mandate.

Valls, 54, is a law-and-order hardliner whose business-friendly economic stance face attack from his rivals from the traditional left of the party in campaigning ahead of the Socialist-led left-wing primaries in late January.

Valls will also have to extricate himself from Hollande’s turbulent five years at the helm of the euro zone’s number two economy if he is to persuade voters he is the best candidate to heal the party’s rifts.

“We must unite: My candidacy is one of conciliation, of reconciliation,” he said.

Valls said his resignation as prime minister would take effect on Tuesday.

Health Minister Marisol Touraine and Interior Minister Bernard Cazeneuve are seen as possible choices to replace him and lead what will effectively be a caretaker government.

Valls said reducing high unemployment would be his priority and he pledged to lower taxes for the poorest and for the middle-class, if elected. He also promised to protect France’s social security system.

He faces a fight for the Socialist nomination. There are now eight candidates, with Valls’ chief rival being former economy minister Arnaud Montebourg, who is popular among the traditional left.

The failure of pollsters to forecast the outcome of the Les Republicains primary, won by Fillon, and the high number of undecided voters on the left mean the race is wide open.

In contrast to the left’s divisions, the right has rallied behind Fillon, a 62-year-old former prime minister and admirer of late British prime minister Margaret Thatcher. He promises to slash public spending, cut half a million public sector jobs and overhaul social security.

“I want to fight, in this campaign, against the right,” Valls said. “With its old recipes from the ‘80s..., it is proposing social regression.”

Even if Valls wins the Socialist nomination, he will face stiff competition not only from Fillon and Le Pen but also from left-wing candidates who have made clear they will not take part in the primaries, including former economy minister Emmanuel Macron and firebrand Jean-Luc Melenchon.