Its latest monthly survey showed that prices slipped 0.5% in July. The monthly dip takes the annual rate to 6.6% compared to 8.7% in the 12 months to June.
A significant fall in prices could severly impact on house building activity as builders seek to shore up profits rather than push volumes.
Martin Gahbauer, Nationwide’s chief economist, said: “So far in 2010 demand from home buyers has made little progress in building upon the recovery seen during much of 2009.
“Despite the introduction of a second stamp duty holiday for the vast majority of first time buyers and record low interest rates, the number of properties changing hands across the UK is still running at only half the levels seen prior to the financial crisis and recession.”
The Nationwide said prices were easing because more homes were being put up for sale but demand from buyers remained subdued.
He added: “At the moment, the market is clearly easing relative to the very tight supply conditions that characterised it since early 2009.
“However, it will take several more months to establish whether house prices are now simply oscillating around a flat price trend or whether a period of downward trending prices may be in store.”
Earlier this week a survey revealed house prices had fallen by 0.1% in – the first decline in 15 months, according to its data.
The report warned that talk of impending public spending cuts is damaging confidence, with a 1.3% fall in new buyers registering with agents and homes now taking 8.7 weeks to sell, which is a return to the period seen last August.