WASHINGTON

U.S. home prices rose at the fastest pace in more than three years in September, lifted by a record-low supply of houses for sale.

The Standard & Poor’s CoreLogic Case-Shiller national home price index released Tuesday rose 6.2 percent in September from a year earlier, the largest gain since June 2014. In 13 of the 20 cities tracked by the index, yearly price gains in September were faster than in August.

Home buyers are desperately bidding up prices because so few properties are available. The number of homes for sale in September was the fewest for that month on records dating back to 2001, according to the National Association of Realtors. And home builders aren’t yet putting up enough new homes to reduce the supply crunch.

Seattle, Las Vegas and San Diego reported the highest year-over-year gains. Home prices jumped 12.9 percent in Seattle, 9 percent in Las Vegas and 8.2 percent in San Diego. Las Vegas, one of the hardest-hit cities in the housing bust, has been making a comeback since prices bottomed out in 2012.

Home prices rose in all 20 cities. The smallest gains were in Washington, D.C., where prices rose 3.1 percent; Chicago, with a 3.9 percent gain; and Miami, at 5 percent.

Unemployment is low and the economy is growing at a solid clip, fueling demand for homes. Mortgage rates also remain historically low, with the average rate on a 30-year mortgage below 4 percent.

Yet Americans are remaining in their homes longer, according to a recent survey by the Realtors. Many are reluctant to sell because there are so few other homes to buy.

Builders are responding to the pent-up demand by building more houses. The construction of new homes jumped nearly 14 percent in October to the fastest pace in a year. But home builders are struggling to find the workers and land they need to ramp up construction more quickly.

“The past two months have shown promising signs of life from builders,” said Svenja Gudell, chief economist at real estate data provider Zillow. “But it’s going to take a lot more than two good months to fully erase the housing deficit we’re facing after years of underbuilding.”

The Case-Shiller index covers roughly half of U.S. homes.