The average price of existing single-family homes in King, Snohomish and Pierce counties rose 0.9 percent in September from the previous month, outpacing the national average price gain, according to S & P/Case-Shiller index data.

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The average price of existing single-family homes in King, Snohomish and Pierce counties rose 0.9 percent in September from the previous month, outpacing the national average price gain, according to S&P/Case-Shiller index data released Tuesday.

September’s monthly home-price gains were higher than August’s, when average home prices in the Seattle metro area rose 0.6 percent from July, after taking seasonal fluctuations into account. The 20-city index in September posted a 0.6 percent gain, marking an acceleration from August’s 0.1 percent increase.

Over the year, single-family-home prices in the Seattle metro increased 8.2 percent, compared with a 5.5 percent increase in the 20-city index, according to S&P Dow Jones Indices, publisher of the index. Annual price gains accelerated in August and September, breaking out of a four-month holding pattern.

San Francisco, Denver and Portland led the 20-city index in year-over-year price growth, posting 11.2 percent, 10.9 percent and 10.1 percent gains, respectively. Phoenix reported its 10th consecutive increase in annual price gains, the longest streak among the 20 metros tracked.

“Home prices and housing continue to show strength with home prices rising at more than double the rate of inflation,” said David Blitzer, chairman of the index committee. “The general economy appeared to slow slightly earlier in the fall, but is now showing renewed strength.”

The recent data show the U.S. housing market is stabilizing, though continued rising prices hurt the affordability of homes, Svenja Gudell, chief economist at Seattle-based Zillow, said in a statement.

“Rising home values and rents alike can make saving a suitable down payment very difficult, and continued shortages in for-sale homes means even qualified buyers with decent savings are often left out in the cold,” she said. “And the threat of rising interest rates may soon put a damper on housing affordability, especially in hotter, coastal markets.”

Average home prices in the King, Snohomish and Pierce counties region are now 4.2 percent below their last peak in July 2007, according to the Case-Shiller index. In the 20-city index, average prices are 11.4 percent off their July 2006 peak.