David Cameron vowed to “stamp out” anti-Semitic attacks in a message to mark the Jewish new year, Rosh Hashanah.

The killing of four hostages at a kosher supermarket in Paris by an associate of the Islamist extremists who attacked the offices of satirical magazine Charlie Hebdo was among recent high-profile incidents.

“As Jewish communities unite in prayer across the world, thoughts will turn to the tragic loss of life that we have seen following a number of horrific and abhorrent anti-Semitic attacks over the past year,” the Prime Minister said in in a video posted on social media by 10 Downing Street.

“Jewish communities will not be left to live in fear. As Prime Minister I will do everything I can to stamp out such hatred now and in the future.”

Campaigners have reported record numbers of attacks on Jews in the UK – with three men and a boy left in hospital after being chased and beaten this month while they waited for a tram in Bury.

Mr Cameron said the Jewish community made an “immeasurable contribution to all areas of British life”.

New Labour leader Jeremy Corbyn – who has been criticised by some in the Jewish community for having links to militants with anti-Semitic views – also sent a message.

“Shana Tova to all – have a sweet and happy New Year,” he wrote on Twitter.

Shadow minister Ivan Lewis earlier said Mr Corbyn had serious questions to answer on his “support for people who engaged in anti-Semitic rhetoric”.

During the election campaign, Mr Corbyn said: “The idea that I’m some kind of racist or anti-Semitic person is beyond appalling, disgusting and deeply offensive.

“I have spent my life opposing racism. Until my dying day I will be opposed to racism in any form.”