WASHINGTON — Home prices rose in May from April in every city tracked by a leading index, a sign that increasing sales and tight inventories are supporting a modest housing recovery.

The Standard & Poor's/Case-Shiller home price index released Tuesday showed increases in all of the 20 cities tracked. And a measure of national prices rose 2.2 percent from April to May, the second increase after seven months of flat or declining readings.

Chicago, Atlanta and San Francisco posted the biggest monthly increases. Detroit, San Diego and Charlotte posted the smallest gains.