House prices grew at the smallest rate possible in June - with the number of homes coming on to the market continuing to push ahead, Nationwide said.
The average cost of a property crept ahead by just 0.1% during the month to stand at £170,111, stoking speculation that the housing market recovery is flagging.
Land Registry figures also out today show house prices in England and Wales fell by 0.2% during May, the first monthly drop for a year.
The Nationwide rise follows a 0.5% rise in May and the bank said property values have now risen by 3% since January.
Martin Gahbauer, Nationwide’s chief economist, said: “Recent indicators point to an increase in the supply of property coming on to the market for sale, perhaps in response to the abolition of Hips in the opening days of the new coalition Government.
“With the level of demand remaining broadly stable, this would in part help to explain the recent slowdown observed in the rate of house price inflation.”
The annual rate at which house prices are rising also fell during June for the second consecutive month.
Nationwide said prices were 8.7% higher during the month than they had been a year earlier, down from a year-on-year rise of 9.8% in May.
The group said the drop reflected the fact that house prices were increasing at a faster pace this time last year.
Land Registry figures
Land Registry figures also out today show house prices in England and Wales fell by 0.2% during May. The fall follows a rise of just 0.1% in April and no change in March, and leaves the average home costing £165,314.
The annual rate of house price growth also fell during the month, dropping to 8.2% compared with 8.5% in April - the first time annual house price inflation has worsened since February last year.
The figures come as property intelligence group Hometrack said house prices edged ahead by just 0.1% during June as demand from potential buyers stalled.
The housing market suffered a slow start to the year due to a combination of the end of the stamp duty holiday, the severe winter weather and uncertainty caused by the general election.
But the market has failed to regain momentum as the impact of these factors has worn off, leading economists to speculate that the recovery may have run out of steam.
The Land Registry figures showed that the number of homes being sold had picked up in March, the latest month for which figures are available, with 48,577 properties changing hands, 37% more than in the same month of 2009.
But the figure still remains well down on the 77,408 sales completed in December.