Sarkozy's announcement comes as the list of candidates to replace Hollande grows and fractures between the Socialists are getting deeper just eight months before the presidential poll.

Government spokesman Stephane Le Foll urged leftist lawmakers on Monday not to place personal ambitions before the party after former industry minister Arnaud Montebourg threw his hat into the ring, saying it was "impossible to support the current president" who had betrayed socialist values.

Montebourg split with Hollande's government in 2014 over his shift in favour of market-friendly reforms. So did former education minister Benoit Hamon and former housing minister Cecile Duflot, a Green, both of whom are also running.

The simmering rebellion has already forced Hollande to allow an unprecedented primary contest to select the party's candidate.

But the increasingly crowded field complicates his re-election prospects should he chose to run for a second term.

A large pool of candidates, ranging from the communists to centre-left, would further dilute Hollande's support base.

Most polls show that if Hollande does run as the left's candidate, he will come third to far-right Front National leader Marine Le Pen and whoever heads the main centre-right campaign.

Splits in the main parties is a gift to the National Front which hopes to convince voters it alone can offer a new form of leadership.

"Montebourg, Duflot, Sarkozy: Why are all those who have governed and failed recently coming back? Do they hope that we have forgotten?," the party's vice-president Florian Philippot said on Twitter.