WASHINGTON » Home prices rose in August in nearly all U.S. cities, and many of the markets hit hardest during the crisis are starting to show sustained gains. The increases are the latest evidence of a steady housing recovery.

The Standard & Poor’s/Case Shiller index reported today that national home prices increased 2 percent in August compared with the same month a year ago. That’s the third straight increase and a faster pace than in July.

The report also said that prices rose in August from July in 19 of the 20 cities tracked by the index. Prices had risen in all 20 cities in the previous three months.

Cities that had suffered some of the worst price declines during the housing crisis are starting to come back. Prices in Las Vegas rose 0.9 percent, the first year-over-year gain since January 2007. Prices in Phoenix are 18.8 percent higher in August than a year ago. Home values in Tampa and Miami have also posted solid increases over the period.

Seattle was the only city to report a monthly decline. Still, prices there fell just 0.1 percent in August from July and are 3.4 percent higher than a year ago.

Prices in Atlanta have fallen 6.1 percent over the 12 months that ended in August, the largest year-over-year decline. But Atlanta has posted the largest price gain among the 20 cities over the past three months, according to Trulia, a housing data analysis firm.

“The sustained good news in home prices over the past five months makes us optimistic for continued recovery in the housing market,” David Blitzer, chairman of the Case-Shiller index, said.

The steady increase in prices, along with the lowest mortgage rates in decades, has helped many home markets slowly rebound nearly six years after the housing bubble burst.

Rising home prices encourage more people to put their homes on the market. They may also entice would-be buyers to purchase homes before prices rise further.

The S&P/Case-Shiller index covers roughly half of U.S. homes. It measures prices compared with those in January 2000 and creates a three-month moving average. The August figures are the latest available.

The figures aren’t seasonally adjusted, so some of the gains in August reflect the benefit of the summer buying season.

Stan Humphries, chief economist at the housing website Zillow, expects the monthly price figures will decline in the fall and winter.

“This doesn’t mean the housing recovery has been derailed,” he said. “This is exactly what bouncing along bottom looks like.”

Other recent reports show that the housing market is improving, albeit from depressed levels.

Home builders started construction on new homes and apartments at the fastest pace in more than four years last month. They also requested the most building permits in four years, a sign that many are confident that home sales gains will continue. Home building is still far below the pace that economists say is consistent with a healthy housing market.

New home sales jumped last month to the highest annual pace in the past two and a half years.

Sales of previously-occupied homes dipped in September but have risen steadily in the past year.