The Prime Minister has expressed his wish that the British Jewish community have a "happy and peaceful Rosh Hashanah" and vowed to defend Israel against its enemies.
David Cameron said he wanted to "pay tribute to the tremendous contribution your community has made to this country and continues to make each year".
Mr Cameron, who has on previous occasions spoken about his Jewish roots, referred to his great-great-grandfather, Emile Levita. A German émigré banker, he became a British citizen in 1871, then married out and sent his sons to Eton.
Mr Cameron said he was incredibly moved by Mr Levita's story. "It made me appreciate all the more what the Jewish community has brought to Britain," he said.
Speaking after he announced that Britain would not take part in the anniversary event marking a decade since the Durban conference on racism, which became a forum for anti-Israel activity, Mr Cameron said he wanted to reaffirm his "unshakable" belief in Israel.
"I know that this New Year comes at a time of particular concern to many events around the world and about the welfare of Israel.
"You have a Prime Minister whose commitment and determination to work for peace in Israel is deep and strong. Britain will continue to push for peace, but will always stand up for Israel against those who wish her harm".
Next week the Palestinians are set to go to the United Nations with a bid unilaterally to declare statehood.
The move is not backed by the US, but the British government has not yet announced its stance.