July home prices rose at the fastest rate in seven years, according to new housing data released Tuesday, but economists say there are signs the housing market is beginning to cool.

Across the country, prices rose 12.4 percent on a nonseasonally adjusted basis compared with the same period last year, according to S&P/Case-Shiller Home Price Indices, which tracks 20 large cities.

But the report also showed that prices grew at a slower rate in July than in June. That may be a sign that the housing market’s breakneck pace of recovery is starting to decelerate.

The stagnation was particularly noticeable in some of the country’s hottest markets. On a monthly basis, July home prices rose 2.8 percent in Las Vegas, the same pace of increase as June. Prices rose by 2.2 percent in San Francisco, down from 2.7 percent in June.

In Washington, however, home prices rose 1.4 percent in July, slightly faster than the 1 percent increase seen in June.

Home prices have been rising for the past two years, as home buyers rushed to make the most of historically low mortgage rates and competed for a limited inventory of homes for sale.

But in the past few months, analysts say, rising mortgage rates may be scaring away some potential buyers. The 30-year fixed-rate is now hovering at 4.5 percent, up from a low of 3.35 percent in January, according to data from mortgage giant Freddie Mac.

Investors who have pounced on cheap rates and rock-bottom home prices to snap up properties are particularly sensitive to such market fluctuations, analysts said.

“The more prices go up, the fewer investors are going to be in the market,” said Greg McBride, senior financial analyst at Bankrate.com. “As prices rise, the rate of return for them is lower.”

Nationally, investors already comprise a smaller part of the market. They bought 17 percent of existing homes in August, down from 18 percent during the same period last year, according to data from the National Association of Realtors.

In the Washington area, cash-only sales have made up a smaller percentage of the market so far this year, 17.5 percent, compared with 18.2 percent a year ago, according to Rockville-based data firm RealEstate Business Intelligence.

There is some variation throughout the Washington region. In Prince George’s County, 27.3 percent of all sales this year were cash only, compared with 17.9 percent of all sales in Montgomery County, according to RBI data. Both counties have seen the share of cash sales fall in the past two years, as home prices rose and more properties moved out of foreclosure.

While cash-only sales are not limited to investors, they usually make up a large chunk of the segment, so analysts use it as a measure of investor activity. The region’s strong demand for rental housing, fueled by the influx of temporary residents, makes it attractive to investors, said Steve Cook, managing editor of a real estate analysis Web site in Silver Spring.

“The Washington area has always been one of the better markets for investors,” said Cook.