WASHINGTON — U.S. home prices rose steadily in May, pushed higher by a healthy increase in sales this year.

The Standard & Poor’s/Case-Shiller 20-city home price index climbed 4.9 percent in May from 12 months earlier, down slightly from a 5 percent pace in April, according to S&P Dow Jones Indices.

Home sales have jumped in recent months as an improving economy boosts hiring and enables more people to afford a purchase. Yet the higher sales haven’t encouraged more people to sell their homes, leaving supplies tight and driving up prices, especially in some cities. According to Case-Shiller, prices rose 10 percent from a year ago in Denver, 9.7 percent in San Francisco and 8.4 percent in Dallas. Washington, D.C. posted the smallest increase at 1.3 percent. Prices rose in all 20 cities from a year earlier.

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

Sales of existing homes increased 3.2 percent in June to a seasonally adjusted annual rate of 5.49 million, the National Association of Realtors said last week. That is the fastest pace since February 2007. Sales are up from an annual pace of just 4.8 million in January.

Some of the accelerated pace has likely been driven by higher mortgage rates and an expected decision by the Federal Reserve to start raising short-term interest rates this year. Most economists forecast that decision will occur in September.

Yet the supply of available homes hasn’t kept up with rising sales. The number of homes listed for sale rose 0.4 percent in the past year, the Realtors said.