The average asking price of homes put up for sale in England and Wales fell for a third month in a row in January, according to estate agents Rightmove.
Rightmove said there were signs that the market was improving
Asking prices were down 0.8% in the five weeks to 12 January but the fall was less than the 3.2% slide seen between November and December.
Annual house price inflation stood at 3.4% in January, its lowest rate since December 2005.
Rightmove said the average asking price for a home now stands at £230,428.
Rightmove said there were some signs that the market was improving in early January despite the fall in asking prices.
"Some homebuyers are now able to find properties that have fallen into their affordability zone, and are bagging what they see as bargains against previous prices," said Miles Shipside, commercial director of Rightmove.
"Some properties have had their prices dropped by 10% or more and are now within reach, satisfying some of the pent-up demand from previous disenfranchised buyers."
Other surveys have also indicated the housing market is slowing.
Recent data from the Department of Communities and Local Government revealed that prices fell by 0.8% in November, compared with a slight rise of 0.1% in October.
The latest research from the Halifax bank and the Nationwide building society suggested the market weakened further in December.
Mortgage approval levels also fell to a three-year low in November.