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)