David Cameron offered his full support to a plan for a new Royal Yacht, but said it should not be publicly funded, it has been revealed.

The prime minister wrote to the chairman of a charitable trust trying to raise £100m for a new national flagship welcoming his "truly inspiring initiative" in October, it emerged on Monday.

The revelation comes after a leaked letter from Education Secretary Michael Gove suggesting that the yacht could be seen as "a gift from the nation to Her Majesty" on the Queen's Diamond Jubilee sparked uproar.

The proposed sailing ship - 650 feet long and as tall as St Paul's Cathedral - would provide education and vocational training for young people, facilities for scientific research and a venue for trade missions and commercial exhibitions as well as staterooms for the use of the Royal Family on trips around the United Kingdom and overseas.

Retired Rear Admiral David Bawtree said he approached universities minister David Willetts with his proposals for a Future Ship Project for the 21st Century last year, who backed the project along with Education Secretary Michael Gove.

Cameron's official spokesman said the prime minster would "react favourably" to requests for government assistance, but believed it would be "inappropriate" for taxpayers' cash to be used on the project.

The PM said that he was keen on projects that aim to help young people from all backgrounds to develop the skills and energy that Britain needs for its future prosperity, the Rear Admiral explained.

His letter said: "I think this is a splendid idea and you have my full support. I know you intend the project to be privately-funded and there is some way to go, but you understand that the government is not able to offer any financial assistance."

Rear Admiral Bawtree, the former commander of Portsmouth's naval base, said he was not seeking state funding, but that Cameron's letter would boost efforts to secure private donations.

Gove also told MPs he was not suggesting using taxpayers' money to fund the project.

"The letter which I wrote to the prime minister on September 12 clearly stated that I agree of course the project for a royal yacht, the Future Ship Project for the 21st Century, was one... where no public funding should be provided," he said.

In his letter, Gove said that the Queen's "highly significant contribution" to Britain and the Commonwealth should be recognised with a "lasting legacy".

But Labour Party deputy chairman Tom Watson said: "When school budgets are being slashed, parents will be wondering how Gove came even to suggest this idea. This is not the time to spend £60m on a yacht."

And Deputy Prime Minister Nick Clegg said: "Most people in the country would think the Diamond Jubilee is a wonderful occasion for us to celebrate together as a community and as a nation.

"But I suspect that most people in the country would think, given that there is very little money around, that this probably would not be the top of their list of priorities for the use of scarce public resources."

A Buckingham Palace spokesman said: "The travel arrangements for the Queen and other members of the Royal Family are handled with great care and in close liaison with government. It would, therefore, be inappropriate to speculate on the future use of any vessel by the Royal Household."

The proposed yacht would see young people spend up to three months on board pursuing studies and assisting a team of around 20 scientists researching the health of the oceans.

The 90,000 square feet of sails could contain photo-voltaic threads allowing it to power itself with solar energy. And the design includes 400 square metres of exhibition space for businesses.