The behind-the-scenes battle over the level of government financial support for ambitious new green energy projects broke out into the open today when Chris Huhne, the energy and climate change secretary, delivered a coded criticism of the Treasury's stance on the issue.

He risked a row with George Osborne's department, after appearing to compare the Treasury's opposition over the green investment bank to its scuppering of a similar stimulus plan backed by the economist John Maynard Keynes in the 1930s. Some economists argue that sticking to more fiscally conservative policies helped to prolong the Great Depression in Britain.

The Liberal Democrat minister, who drew the analogy at a private meeting of City financiers, was careful not to criticise the Treasury directly. It is understood that he acknowledged media reports of the differences with the Treasury on the issue without denying them.

Uncertainty over the bank's future has also prompted a furious response from a member of the Green Investment Bank Commission, who wanted to remain anonymous. The commission was set up by Osborne in February to advise the Treasury. The member said it was essential that it was able to raise money by issuing government-backed bonds: "Frankly, if it doesn't there's no point in it existing. If we were only ever going to do one thing, the green bond is the thing we need to do."

He added: "It is now an imperative nationally and internationally that governments fund these banks and get on and fund climate change projects because if they don't we won't have a planet. It's a simple as that."

Today, in answer to questions from MPs on the Commons liaison committee, David Cameron said he would back the bank. Asked whether it was "truly going to be a bank" and not a fund, whether there was the risk of dispute between the Department of Business and the Treasury, and whether he would take a personal interest in the issue, he said: "Yes, yes and yes, to all of those." The nature of how the bank would operate was not covered.

Negotiations over the green investment bank are complex and at a sensitive stage, involving several government departments. Huhne and other backers of the plan are anxious not to antagonise Osborne or powerful officials at the Treasury, whose approval is required for it to go ahead.

The Lib Dems and the Conservatives committed to the establishment of a bank in the coalition agreement, but the Treasury's priority of reducing the deficit has led to serious differences within Whitehall over how much government financial backing the bank should have.

Pressure appears to be growing across government departments on the Treasury to sanction a fully functioning green investment bank. But no breakthrough has been made and frustration is growing in Whitehall and the City over the slow pace of negotiations.

Huhne has been championing the establishment of a green investment bank which would be able to help deliver the estimated £200bn of investment in clean power plants, offshore windfarms and smart grids required by 2020. He wants a bank able to leverage capital from the private sector – for example by issuing "green bonds" – to invest in riskier projects at the early stage. Such a bank would probably have to offer investors either an implicit or explicit government guarantee.

Some officials at the Treasury remain opposed to the idea of a government-backed bank taking on billions of pounds of liabilities adding to the deficit and want a more limited bank.

At the Wednesday morning meeting, Huhne who had a successful career in the City and was an economics journalist before entering politics, outlined his vision for the bank. He drew the analogy with the "Macmillan Gap" identified in 1931 by a government-appointed commission, which included Keynes. It proposed establishing a government-backed bank to finance smaller British businesses, which were struggling to cope with the global depression and could not secure finance from banks.

The fiscally conservative Treasury resisted the proposal, Huhne told his audience. It was not until 1945 that the Industrial and Commercial Finance Corporation was set up, which eventually became 3i Group, one of Europe's leading private equity groups.

Huhne did not directly say that current Treasury officials have a similarly cautious fiscal mindset, but it is understood that the audience of mostly bankers and City investment managers was left in no doubt of the message he was sending.