In a response to a Commons' Select Committee report into the Building Schools for the Future programme, which aims to rebuild or refurbish all secondary schools by 2020, it said: "Our initial research indicates that with current technologies, zero carbon schools can only be achieved at considerable extra cost, and even then site constraints mean that zero carbon cannot be achieved in all cases.
"The level of capital investment would exceed any potential savings in school running costs."
The Department for Children, Schools and Families previously said new schools would only receive funding if they were designed to produce no carbon footprint.
Sally Brooks, head of school capital at the department, told a conference earlier this year: "This is the first government programme where funding is dependent on carbon neutrality."
However, new schools will only be expected to reduce their carbon output by 50 per cent by using renewable energy, the Government said. Schools will off-set the rest.
Ministers were keen to promote the building programme's green credentials. They invested pound;110 million in April to deliver 200 eco-schools over the next three years.
The statement came as the Government was reported to be on the verge of abandoning a target of 20 per cent of European energy to come from renewable sources.
The Government also told the select committee that consultants PricewaterhouseCoopers would produce a report on the impact of BSF on pupil achievement this year.
l Nottinghamshire has reduced carbon emissions by 4,000 tonnes by using wood pellets instead of fossil fuels to heat its schools. The boilers are used to teach primary school pupils about climate change.