The Case-Shiller index measures repeat sales of single-family homes. The September figures are the latest available.

Home prices climbed 5.5 percent annually and 5.1 percent from August, the 53rd consecutive month of positive gains. Seattle; Portland, Ore., and Denver had the biggest year-over-year gains among the 20 cities. Seattle had an 11 percent annual increase, while Portland had a 10.9 percent increase and Denver an 8.7 percent increase. Washington had one of the smaller increases, rising 2.7 percent.

“The new peak set by the S&P Case-Shiller CoreLogic National Index will be seen as marking a shift from the housing recovery to the hoped-for start of a new advance,” David M. Blitzer, managing director and chairman of the index committee at S&P Dow Jones Indices, said in a statement.

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After peaking in July 2006, home prices bottomed out in February 2012. The most harmful result of the housing bust was the steep decline in home values, which left millions of homeowners owing more on their mortgages than their homes were worth. The steady rise in home values, which began in 2013, has been good news for underwater borrowers. But it has made homeownership less affordable for others.

Low mortgage rates have helped fuel the rise in prices as has a limited supply of homes for sale.

Bill Banfield, Quicken Loans vice president, dismissed fears the housing market was experiencing another bubble.

“With home prices growing to record highs, it’s important to remember this isn’t driven by speculation or easy credit like a decade ago,” Banfield said. “It is led mostly by constrained home availability as buyers continue to battle over the few homes for sale, especially in the West. We may see a retreat in home prices when supply opens up, increasing choice for buyers and the health of the housing market.”

Although prices have bounced back, many economists tempered their enthusiasm about what it means for the housing market’s overall health.

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“Crossing this threshold is largely symbolic,” said Ralph McLaughlin, Trulia chief economist. “The housing market recovery has been very uneven across the U.S. When controlling for inflation, markets that have reached their pre-recession peaks are few and almost exclusively in the West and South. And within those markets, it’s most high-end homes that have surpassed the peak.”

McLaughlin noted that Pittsburgh and Buffalo are the only two markets outside the South and West where home prices have recovered to pre-recession levels and that recovery is limited to trade-up and premium homes.

Zillow chief economist Svenja Gudell echoed McLaughlin’s sentiments.

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“The U.S. National Case-Shiller home price index has essentially regained all losses sustained during the housing bust and is at, above or very near peak levels in many markets,” she said. “But it isn’t smart to confuse this full recovery in housing prices with a full recovery in the housing market overall. Big imbalances still exist between renters and homeowners, and home buyers and home sellers, and there’s still a long way to go before the market reaches full equilibrium.”