Tim Melville-Ross, chief executive of the Nationwide, said it would be in the longer-term interests of housing if mortgage interest tax relief - which will cost the Treasury pounds 5.8bn this year - were phased out over several years.
However, he argued that first-time buyers should be allowed a temporary increase in the pounds 30,000 ceiling on relief to stimulate recovery in the property market.
In an interview for the Channel 4's Answering Back, to be broadcast tonight, Mr Melville-Ross said it was unsatisfactory that tax relief could be claimed regardless of income. Its removal would cut government borrowing, allowing interest rates to fall.
Accusing the Government of lacking a coherent housing policy, he supported calls for a means-tested benefit for home-buyers with low incomes. He said this would solve the problems of owner-occupiers in arrears.
His views contrast with those of other bank and building society leaders, including Lord Alexander, chairman of National Westminster Bank, and Donald Kirkham, the Woolwich's chief executive, who have argued that the ceiling on relief should be doubled.
However, Richard Best, director of the Joseph Rowntree Foundation, which sponsors independent research into the housing market, said a reduction in the rate of tax relief from 25 per cent to 20 per cent would save the Exchequer pounds 1.2bn a year.
'That alone would cover the cost of a mortgage benefit scheme, enable the Government to give more help to first-time buyers and leave something in hand to stimulate growth in the rented sector,' he said.