A national gauge of prices rose 0.7% in September from August, according to seasonally adjusted data from S&P CoreLogic Case-Shiller. It was the eighth straight month of gains for the index, which doesn't provide a specific dollar figure for homes.

Mortgage rates above 7% have chilled the housing market, keeping both would-be buyers and sellers on the sidelines. Shoppers determined to land a purchase often get dragged into bidding wars for the scant supply of listed properties. The persistent inventory crunch has driven prices up since the bottom in January.

"Although this year's increase in mortgage rates has surely suppressed the quantity of homes sold, the relative shortage of inventory for sale has been a solid support for prices," Craig Lazzara, managing director at S&P Dow Jones Indices, said in a statement Tuesday.

On a year-over-year basis, prices climbed 3.9% in September, compared with a 2.5% annual increase in August.

Detroit, San Diego and New York were among the cities with the biggest price gains. The western part of the US remained the weakest, the data showed. 

New listings have been ticking up recently, and mortgage rates have declined after peaking early this month, signs that some conditions are improving for homebuyers. In the four weeks through Nov. 19, new listings increased 5.2% from a year earlier, the biggest gain in more than two years, according to a report by Redfin Corp.