The skyrocketing rise of U.S. home prices began to slow this summer, quelling fears of a real estate bubble, according to a new report from real estate portal Zillow, but the Boston market continued to outpace the rest of the country.

The Zillow’s Home Value Index stood at $163,000 as of the end of the third quarter for the average U.S. home, up 6.4 percent year-over-year and 1.2 percent from the end of the second quarter, but unchanged from August. The quarterly pace of appreciation was roughly half that experienced in the second quarter.

For months, a handful of already expensive metro areas that experienced relatively modest declines during the crash but very robust gains during the recovery, particularly in California, have flirted with being in a bubble, according to Zillow. But over the summer, price increases began to abate in several of these cities, with home prices in the third quarter actually falling in San Diego (-1.2 percent), Los Angeles (-1.1 percent) and San Francisco (-0.1 percent). Earlier in the year, prices in all three cities were rising at about 3 percent a month.

In Boston, prices continued to rise, but at a slower pace. The median price in Beantown increased 0.5 percent from August to September according to Zillow’s index. Prices were flat in the U.S. as a whole over that same period.

"Far from being a negative sign, we’re relieved to see more noticeable signs of cooling in the market. If home values continued to rise as they have, relatively unchecked, we would almost certainly be headed into another bubble cycle, and nobody wants that," Zillow Chief Economist Stan Humphries said in a statement. "This is more proof that the market recovery is entering a new phase, transitioning away from the bounce off the bottom we’ve been experiencing and finding a more sustainable level. This moderation should help consumers feel more at ease in their decisions to buy and sell, and will help keep the market balanced."

Despite falling monthly appreciation, home values in most areas continue to grow year-over-year. All 30 of the largest metro areas experienced annual gains in September, with the largest coming in Sacramento, Calif. (34.1 percent); Las Vegas (33.3 percent); and Riverside, Calif. (31.8 percent). Annual appreciation is expected to slow markedly over the next 12 months as moderation spreads to an annual pace of 3.8 percent nationwide by September 2014, according to the Zillow Home Value Forecast.