U.S. home prices rose steadily upward in February as more homebuyers chased fewer available properties, a trend that many analysts say may not be sustainable.

The Standard & Poor's CoreLogic Case-Shiller national home price index, released Tuesday , increased 5.8 percent in February, the most in 32 months. Such strong price gains and slightly higher mortgage rates may eventually cool off demand.

But for now, sales of new and existing homes 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 have also 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 cities with the biggest annual price gains in February were Seattle; Portland, Oregon; and Dallas.

Still, some relief may be on the horizon, though it's not clear when. Average rents are leveling off, which could keep many people in apartments and dampen demand for homes.

Mortgage rates are also up from last year's record lows. Those two trends "could put a dent in home-buyer demand and overall price growth," said Svenja Gudell, chief economist at real estate data provider Zillow. "Those changes won't necessarily be unwelcome, especially in some rapidly growing coastal markets in which buyers, sellers and renters could all use a breather."

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.

Home builders are ramping up construction to meet the healthy demand, which may provide buyers some relief. Ground breakings on new homes rose 8.1 percent in the first three months of this year compared with 2016.

And the supply of new homes available for sale in February climbed to a seven-year higher of 266,000.