WASHINGTON — U.S. home prices rose 12.1 percent in June from a year earlier, nearly matching a seven-year high, and prices in Dallas-Fort Worth once again reached an all-time high, according to the latest Standard & Poor’s/Case-Shiller report.Still, month-over-month price gains slowed in most markets nationwide, a sign that higher mortgage rates may weigh on the housing recovery. The S&P/Case-Shiller 20-city price index slowed only marginally from May’s year-over-year gain of 12.2 percent, the fastest since March 2006. And all 20 cities posted gains from the previous month and compared with a year ago, according to the report released Tuesday. Home prices in Las Vegas soared 24.9 percent from a year earlier to lead all cities. Purchases by investors have helped drive that increase. Other cities hit hard by the housing bust also posted stunning gains in the past year. Prices have jumped 24.5 percent in San Francisco and nearly 20 percent in Los Angeles and Phoenix. In Dallas-Fort Worth, prices have increased by 8 percent since June 2012 and gained 1.7 percent from May.In cities less affected by the housing crisis, gains have been more modest. Prices in New York and Cleveland are about 3 percent higher than a year earlier. Prices rose 5.7 percent in Washington, D.C., and 6.7 percent in Boston.Most economists expect the overall index to slow to single digits in the coming months, which they see as a more sustainable pace. “The fundamentals of the housing market are solid,” said Gus Faucher, senior economist at PNC Financial Services. “Despite higher prices and mortgage rates, affordability is still much better than it was prior to the housing crash. … Many households that put off buying a home in recent years are now getting back into the market, boosting demand. Lending standards for mortgage loans are easing somewhat.” The 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 June figures are the latest available. They are not adjusted for seasonal variations, so the monthly gains reflect more buying over the summer. Steady job gains and low mortgage rates have encouraged more Americans to buy homes. And even as demand has risen, a limited number of homes have been available for sale. That combination has led to sharp price gains. But mortgage rates have climbed more than a full percentage point since May. The increase has already slowed sales of new homes in July. And economists expect that it could drag resales lower in August. A slowdown from the strong price gains in recent months isn’t necessarily a bad thing, said Stan Humphries, chief economist at real estate data provider Zillow. It may keep homes from becoming unaffordable. “This ongoing stabilization … is happening, and it’s not the end of the world for the housing market,” Humphries said.