Home prices rose modestly in January, according to a closely watched index released Tuesday, but some housing industry analysts remain concerned about the sustainability of the housing sector rebound.

Home prices in 20 cities tracked by the Standard & Poor’s/Case-Shiller Home Price Index rose 0.3 percent on a seasonally adjusted basis in January, compared with December. That was the eighth consecutive monthly increase in the index. Compared with the same period last year, prices were down 0.7 percent.

“We need to see house prices improving, so it’s a good start on that,” said Robert Dye, a senior economist at PNC Financial Services Group.

On a seasonally adjusted basis, prices were up the most in Los Angeles, 1.8 percent, and San Diego, 0.9 percent, compared with the previous month.

But the news wasn’t all good. The Case-Shiller index measures a three-month average of prices, so January’s report includes data from November when homes sales were strong, helping blunt price declines.

Overall, home prices are at 2003 levels.

The report is “mixed,” analyst David Blitzer of Standard & Poor’s said in a written statement. The “rebound in housing prices seen last fall is fading.”

Analysts are worried that an expected increase in the number of foreclosed properties hitting the market could put pressure on prices later this year. Also, a Federal Reserve program that has kept interest rates low ends today. If mortgage rates rise later this year as expected, some potential buyers could decide to stay on the sidelines.