The suggestion drew a furious response from ministers and caused a rift between senior figures at the Holocaust Educational Trust (HET), which organises the trips. The Tory leader was heavily criticised by HET chairman Lord Janner, a Labour peer, who urged him to retract the accusation.

"The Jewish community will be deeply hurt and offended by this," the Labour peer said. "It's a low form of politics which David Cameron must already be regretting. I think it's very, very important that he apologises."

Schools Secretary Ed Balls also seized on Mr Cameron's criticism of 26 "short-term gimmicks" under Prime Minister Gordon Brown, including "trips to Auschwitz".

But the Tories insisted that the leader's remarks had been directed only at government funding arrangements and not the visits themselves. In particular, they criticised that £4.65 million set aside by ministers to fund visits by two students from every further education institution in the country would not meet all the costs.

Schools will be required to put £100 towards the cost of each youngster's trip to the Nazi concentration camp - a top-up which the Conservatives promised to scrap.

Lord Hunt of Wirral, vice president of the HET, said there was genuine concern about the funding and attacked Labour for trying to score party political points.

He said the issue of conditions attached to the funding, which had not been made clear at the time of the announcement earlier this month, had been raised within the trust.

But a Conservative Party spokesman said: "David Cameron's speech sets out very clearly the context of his argument. School trips to Auschwitz are a brilliant idea. However, by announcing these trips without providing the necessary funding the Government has - in classic fashion - hidden the detail in the small print.

"Under a Conservative government these trips would be funded in full and schools would not have to find £100 per pupil from their budgets."