Home prices in 20 cities climbed in June for the first time since a tax credit boosted sales in 2010, indicating the industry is starting to rebound.

The S&P/Case-Shiller index increased 0.5 percent from June 2011 after falling 0.7 percent in the year to May, a report showed yesterday. The last 12-month increase took place in September 2010. Nationally, prices jumped last quarter by the most in more than six years.

The lowest mortgage rates on record and a decline in sales of distressed properties may help the market contribute to the economic expansion that is now in its fourth year.

A more sustained rebound may require easier lending conditions, which would also give consumers a lift.