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Home prices in Chicago and around the country climbed in February as more homebuyers chased fewer available properties.

The Standard & Poor’s CoreLogic Case-Shiller national home price index increased 5.8 percent in February, the most in 32 months. Chicago has been a laggard compared with many of the 20 large cities tracked by Case-Shiller, but in February home prices in the metro area pulled ahead of the national average. Prices in Chicago were up 6.2 percent. Chicago prices have been picking up while cities that have been experiencing huge gains for months slowed.

The cities with the biggest annual price gains were Seattle; Portland, Ore.; and Dallas.

Strong price gains and slightly higher mortgage rates may eventually cool off demand.

But for now, sales of new and existing homes across the country are robust. Last month, sales of existing homes reached their highest level in a decade. The strong demand, however, hasn’t enticed more Americans to sell their homes. The number of houses for sale has dropped to its lowest level in nearly 20 years, which makes finding an available home the toughest challenge awaiting potential buyers in the spring home buying season.

Many homeowners have benefited from the sharp price gains of recent years, but those increases also have made it harder for them to “trade up” to a bigger house, discouraging them from selling. Others have very low mortgage rates and may be reluctant to sell if doing so would force them to take on higher borrowing costs.

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 February figures are the latest available.

Gail MarksJarvis contributed.