A plan by the education secretary, Michael Gove, to send a copy of the King James Bible to every school in the country – each including a personal inscription from him – has run into trouble after government sources reported he has been told to find private funding for the project.

Sources said David Cameron told Gove that while he supported the idea, the education secretary should avoid using taxpayers' money for it. But Gove has yet to find a private philanthropic sponsor for the enterprise, and some Whitehall sources said he has been told he cannot distribute the book until he does so, leaving thousands of copies in a warehouse abroad.

The Department for Education denied aspects of the story, but said they did not know if the copies had yet been printed, or where the copies might currently be stored. They added the Bible was always intended to be distributed to schools at Easter, so there had been no slippage in the timetable due to the lack of a sponsor.

Education department officials said the prime minister supported the plan and said they did not recognise accounts of a conversation in which Gove was told no taxpayers' money could be used. But Whitehall sources said Gove was told at the highest levels that it would be wrong to spend nearly £400,000 on the project at a time when the government was in negotiations with teaching unions over cuts to their pension entitlement.

Education department officials insisted the bibles would be distributed before Easter even if no sponsor had been found. A senior education department source said enough public cash was available to press ahead and No 10 had merely indicated that "sponsorship was desirable". A Department for Education official said in a statement: "The prime minister was clear in his speech in December about the importance of the King James Bible, and marking this important anniversary. The prime minister supports the plan to send a copy to every school. We continue to seek philanthropic sponsorship."

The 400th anniversary of the publication of the Bible was in 2011.

Earlier this week, Gove emerged as an enthusiastic supporter of plans for a new royal yacht to mark the Queen's diamond jubilee. He has insisted unambiguously in one letter that no taxpayers' money will be involved in the yacht project , but in another to cabinet ministers his wording appeared to suggest that public funding was an option.

Questions have been asked whether the upkeep, running costs and security surrounding a royal yacht would fall on the public purse. Gove has been both lauded and ridiculed for his support for the yacht, and has faced a similar divided response for his support for the King James Bible distribution.

In a speech in December, Cameron celebrated the importance of the King James Bible giving three reasons for its relevance.

He said: "The King James Bible has bequeathed a body of language that permeates every aspect of our culture and heritage. Second, just as our language and culture is steeped in the Bible, so too is our politics. Third, we are a Christian country. And we should not be afraid to say so. Let me be clear: I am not in any way saying that to have another faith – or no faith – is somehow wrong."