PARIS (Reuters) - French President Francois Hollande told the authors of a book just published that "France has a problem with Islam", comments that risk dividing his party before next year's presidential election.

Hollande made the remarks to the two authors of "A President Shouldn't Say That...." in December 2015, a month after Islamist militant gunmen and bombers attacked Paris, killing 130 people. Their book was published on Wednesday.

"It's true that there's a problem with Islam. No one doubts it," Hollande is quoted as saying.

"It's not that Islam poses a problem in the sense that it is a dangerous religion, but in as far as it wants to affirm itself as a religion of the Republic."

The comments echo similar statements by conservative politicians following a fresh wave of militant attacks this summer, though Hollande did not suggest the hard-line responses advocated by some right-wing opponents.

Among other proposals, former President Nicolas Sarkozy, who is seeking a return to the Elysee palace, has promised a nationwide ban on burkinis and said France should detain or tag all individuals on an intelligence watchlist.

Since the late 1980s, successive Paris governments have tried but failed to nurture a liberal "Islam of France" that would help integrate the faith into secular society. In August, Prime Minister Manuel Valls said the state must re-invent its relationship with the "Islam of France".

Asked about Hollande's comments, government spokesman Stephan Le Foll said: "There's a problem with Islam today because Islam is politicized by some. There is a problem and at the same time we need to be able to overcome this problem."

The book was written by two respected journalists, Gerard Davet and Fabrice Lhomme, who met with Hollande 61 times. Opposition politicians said on Wednesday that Hollande, France's most unpopular president in six decades, should spend less time talking to journalists and more time governing.

The release of the book eclipsed any media boost for Hollande from a wide-ranging interview with L'Obs magazine also published on Wednesday, which people close to him said was supposed to take him a step closer to formally launching a bid for re-election.

Late on Wednesday, Hollande invited two of France's highest ranking judges to see him to patch up relations after the book also quoted him disparaging judges, according to a tweet on the top appeals court's Twitter account.

Hollande sits atop a deeply divided ruling Socialist Party and has not yet declared if he will run for re-election. Should he chose to, he will face several challengers for the party's nomination.

(Reporting by Elizabeth Pineau, Additional reporting by Emmanuel Jarry, Writing by Richard Lough, Editing by Leigh Thomas, Larry King)