Home prices increased in September in most major U.S. cities, more evidence of a housing recovery that is providing a lift to the fragile economy.

The Standard & Poor’s/Case Shiller national index measuring prices in 20 cities rose 3 percent in September compared with the same month a year ago. Prices also gained 3.6 percent in the July-September quarter compared with the same quarter in 2011. (Read More: Yes, Housing Starts Surge, but Rentals Are the Drivers)

Across the nation, prices increased in 18 of 20 cities.

Phoenix prices jumped 20.4 percent over that stretch to lead all cities. Prices in Atlanta showed a modest 0.1 percent increase, ending 26 straight consecutive year-over-year declines.

Prices also rose in September from August in 13 cities. Five metro regions posted declines, and two were unchanged. Monthly prices are not seasonally adjusted.