Saverne (France) (AFP) - French prosecutors said Monday they had taken five teenagers into custody suspected of vandalising hundreds of Jewish graves, an act that prompted fresh pleas for Jews not to turn their back on France.

The boys are aged between 15 and 17 and all come from Sarre-Union in Alsace, eastern France, where around 300 tombs were defaced and damaged on Thursday.

The youngest came forward after seeing the scale of the reaction across the country to the vandalism, prosecutor Philippe Vannier said.

"Apparently, he was very, very affected by the scale of the reaction to this affair, including the statements from the highest state authorities," Vannier told reporters.

French President Francois Hollande will visit the area on Tuesday.

The boy, who was encouraged to hand himself in by one of his friends, has denied any anti-Semitic motive, Vannier added.

"We don't know the motives of these adolescents who don't have past criminal records and we don't know of any ideological convictions that could explain their behaviour.

"They are very, very shocked by the turn of events."

The five boys pushed over tombstones in the cemetery and opened up vaults. A monument to the victims of the Holocaust at the entrance was also vandalised.

- 'A despicable act' -

The incident was widely condemned by French leaders on Sunday.

Interior Minister Bernard Cazeneuve called it "a despicable act", while Prime Minister Manuel Valls described it as "anti-Semitic" on Twitter.

The vandalism has contributed to an increasing sense of insecurity among French Jews, who were also targeted during the jihadist attacks in Paris last month.

As with previous incidents, Israeli Prime Minister Benjamin Netanyahu took the opportunity to call on Europe's Jews to emigrate.

"To the Jews of Europe and to the Jews of the world I say that Israel is waiting for you with open arms," Netanyahu said.

And as with his previous statements, the call triggered an irritated response from Valls, who noted Netanyahu was "in the middle of an election campaign" ahead of a vote on March 17.

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"The place for French Jews is France," stressed Valls.

Valls also urged national "unity" in the face of what he called "Islamo-fascism", a choice of words that has raised eyebrows in France.

"To combat Islamo-fascism, for that is what it should be called, our strength must come from unity," he said.

France is home to Europe's largest Jewish population and also the continent's largest Muslim population, although it is difficult to give precise figures as the French state is officially secular and does not collect data based on religion.

Last month, the country's main Jewish group said the number of anti-Semitic acts doubled in France during 2014, with acts involving physical violence leading the increase.

Some 851 anti-Semitic acts were registered in 2014, compared with 423 the previous year, with acts of physical violence jumping to 241 from 105, the CRIF said.

Last week's vandalism is not the first time a Jewish cemetery in Sarre-Union has been targeted.

In 1988, around 60 Jewish steles were knocked over, and 54 tombs were wrecked in 2001.