Prices nationally climbed 6.4% from a year earlier, an S&P CoreLogic Case-Shiller index shows. That's larger than the 6% annual gain in January. 

Purchasing a home is more expensive than ever in many areas of the country after run-ups in both prices and mortgage rates over the past couple of years. While new listings have ticked up recently, giving buyers more choices, inventory is still stuck well below historic levels, so competition remains intense. 

"Following last year's decline, U.S. home prices are at or near all-time highs," Brian Luke, head of commodities, real and digital assets at S&P Dow Jones Indices, said in a statement Tuesday. "For the third consecutive month, all cities reported increases in annual prices, with four currently at all-time highs: San Diego, Los Angeles, Washington, D.C., and New York."

A measure of values in 20 cities was up 7.3% from a year earlier. San Diego continued to show the biggest annual gain, with prices soaring 11.4%. Chicago and Detroit followed, with increases of 8.9%.

The Northeast region — including Boston, New York and Washington — ranks as the best-performing market over the past half-year, according to Luke. 

"As remote work benefited smaller (and sunnier) markets in the first part of the decade, return to office may be contributing to outperformance in larger metropolitan markets in the Northeast," he said.

A study released this week by Bankrate showed buying a home is more expensive than renting in all of the country's 50 biggest metropolitan areas. The typical monthly mortgage payment on a median-priced home is about 37% more than the typical rent bill, according to Bankrate, which analyzed data from Redfin and Zillow.