U.S. home prices jumped 10.9 percent in March compared with a year ago, the most since April 2006. A growing number of buyers are bidding on a tight supply of homes, driving prices higher and helping the housing market recover.

The Standard & Poor’s/Case-Shiller home price index released Tuesday also showed that all 20 cities measured by the report posted year-over-year gains for the third straight month.

And prices rose in 15 cities in March from February. That’s up from only 11 in the previous month. The monthly figures aren’t seasonally adjusted and may reflect the beginning of the spring buying season.

Prices rose in Phoenix by 22.5 percent over the past 12 months, the biggest gain among cities. It was followed by San Francisco (22.2 percent) and Las Vegas (20.6 percent).

New York City had the smallest year-over-year increase at 2.6 percent, followed by Cleveland at 4.8 percent.

“Rising home prices may begin to alleviate a lack of housing inventory … by encouraging more homeowners to put their properties on the market,” said Maninder Sibia, an economist with Economic Advisory Service, in a note to clients. “The housing market is clearly improving.”

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 March figures are the latest available.

The U.S. housing market is steadily recovering, buoyed by solid job gains and near-record low mortgage rates. Sales of new homes rose in April to nearly a five-year high. And sales of previously occupied homes ticked up in April to the highest level in three and a half years.

Despite the gains, a limited number of homeowners are putting their houses on the market. That’s helped lift home prices. And it’s made builders more willing to ramp up construction. Applications for building permits rose in April to the highest level in nearly five years.