Annual home-price gains fell below 6% for the first time in a year in August, another sign that the slowdown in the housing market is becoming widespread and is likely to persist in the months to come.

The S&P CoreLogic Case-Shiller National Home Price Index, which measures average home prices in major metropolitan areas across the nation, rose 5.8% in the year ending in August, down from a 6% year-over-year increase reported in July.

Price gains accelerated for most of the last two years, growing significantly faster than both incomes and inflation. August marked the fifth straight month of decelerating price gains, as interest rates have risen and inventory in some markets has been growing.

Home buyers “must be breathing a collective sigh of relief that home price growth finally has slowed.” said Skylar Olsen, director of economic research and outreach. Ms. Olsen said the slowing appreciation “is a sign that fierce competition is dying down.”

The Case-Shiller 10-city index gained 5.1% over the year, down significantly for the second straight month from 5.5% the prior month. The 20-city index gained 5.5%, down from 5.9% the previous month.

Fourteen out of 20 cities are showing slower price growth than a year earlier.

Las Vegas had the fastest home price growth in the country for the third straight month, at 13.9%, followed by San Francisco, where prices grew 10.6%. Seattle, where realtors have reported a significant pullback in buyer demand in recent months, fell to third place with a 9.6% annual gain in prices.

David Blitzer, managing director at S&P Dow Jones Indices, said that even though there is a pullback in the housing market there are no signs that the current weakness will become a repeat of the crisis in 2008 because mortgage default rates remain low. “Without a collapse in housing finance like the one seen 12 years ago, a crash in home prices is unlikely,” he said.

More than five years of rapidly rising prices, combined with higher mortgage rates are making homes increasingly unaffordable for buyers. Rates for a 30-year mortgage averaged 4.86% last week, up nearly a full percentage point from the beginning of the year, Freddie Mac said last Thursday. Because Case-Shiller home-price data lags behind by a couple of months, it doesn’t yet reflect the most recent run-up in rates.

“Coupled with mortgage rate increases that picked up steam in September, higher prices are stifling home sales as more buyers are priced out of the market,” said Danielle Hale, chief economist for Realtor.com.

Most sectors of the housing market are slowing, including new home sales and housing starts. Sales of previously owned U.S. homes fell 3.4% in September from the previous month to a seasonally adjusted annual rate of 5.15 million, the National Association of Realtors said Friday.

Fewer people are attending open houses and inventory levels are rising, prompting Lawrence Yun, the group’s chief economist, to acknowledge there has been a “clear shift” in the market.