David Cameron's plan to "make the dream of home ownership a reality" through state-backed 95% mortgages has been overshadowed on its first day by MPs warning that the scheme could pose a threat to financial stability.

The prime minister promised the Help to Buy scheme would help thousands of people to "put down roots and raise a family" by allowing them to buy a house worth up to £600,000 with a deposit of just 5%. The government will guarantee up to 15% of the loan, in return for a fee from the lender, potentially lowering the average deposit needed from more than £40,000 to just over £10,000.

But the launch of the scheme was overshadowed by a warning from the chairman of the Commons Treasury select committee, Andrew Tyrie, who said any mistakes in the scheme could "carry threats to financial stability".

He is one of many senior politicians, including Vince Cable, the business secretary, who have warned the scheme could cause problems such as fresh housing bubble.

Despite these fears, RBS and NatWest are launching their first offers on Tuesday with "no fee" deals attracting interest rates of 4.99% for two years or 5.49% for five years. Experts said the rates appear to be well-priced even though there are already a few deals on the market for 95% mortgages. Halifax and Bank of Scotland will be ready for the scheme by the end of the week, while Virgin Money and Aldermore Bank plan to begin their offers next year.

On Monday night, Cameron launched a firm defence of the scheme as a way to help "people who can afford the monthly mortgage payments but haven't got rich parents and can't pay the deposit up front".

"There is a need for government to act," he said. "Buying your first home is about far more than four walls to sleep at night. It's somewhere to put down roots and raise a family. It's an investment for the future. Above all, it's a sign that everything you've put in has been worth it."

George Osborne, the chancellor, added that the scheme is aimed at "those families that have saved for years" and young people who should have "the same chance of getting on the property ladder as their parents and grandparents".

The Tories brought forward the launch of the scheme by three months at their autumn conference last week, despite a string of warnings about its potential effect on house prices.

Treasury ministers have tried to head off concerns about a house price bubble by saying they will hold annual reviews to make sure the scheme is operating safely. However, the Treasury committee warns the government has yet to allay concerns about how the guarantee scheme will run and end.

It said the Bank of England must be allowed to put the brakes on the Help to Buy scheme at any time if it threatens a dangerous housing bubble, rather than simply being subject to a review once a year. The MPs said they were concerned that the primary effect of the scheme "could be to raise house prices rather than to stimulate new supply".

"Given the chequered history of government interventions in residential property, great care will need to be taken in both the construction and running of this scheme," Tyrie warned. "Mistakes could distort the housing market or carry threats to financial stability."

Although the scheme is only set to run for three years, the commitee said the government could also come under "immense" political pressure to extend it if it proves popular.

The scheme has already fuelled a surge in interest from homebuyers, pushing up prices across the country, according to a wide-ranging survey of estate agents. A monthly report from the Royal Institution of Chartered Surveyors (Rics) said prices in September were up for a fifth consecutive month as buyers return to the market in their biggest numbers for four years. Banks are even extending their opening hours in anticipation of extra demand.

David Hollingworth, of London & Country Mortgages, said the NatWest and RBS rates are "certainly well priced against the meagre competition in the market at the moment".

"The scheme's aim was to offer more choice and at better rates, so these deals do seem to tick the boxes," he said. "It's now a case of seeing if they are low enough to attract borrowers to the market in increased numbers."

The Treasury fees for offering the scheme to banks and building societies will work on a sliding scale depending on the loan-to-value ratio of the mortgage being offered. The highest charge will be on 95% loans, as these pose the biggest risk of going wrong. It has been reported that lenders could pay around 0.9% of the total amount, being borrowers, to guarantee a slice of the loan equivalent to 15% of the purchase price. On a mortgage of £150,000, that would cost the lender £1,350 to guarantee £23,700. The fees may end up being passed on to customers.