Home prices rise by the most since early 2006

Since April, all 20 cities are up month to month.

In addition, all 20 cities posted gains in July from the previous month and compared with a year ago, even though 15 cities and both indexes saw their monthly rates decelerate in July versus June.

"However, the monthly rates of price gains have declined," he said. "More cities are experiencing slower gains each month than the previous month, suggesting that the rate of increase may have peaked."

The Southwest continues to lead the housing recovery. 

Las Vegas home prices soared 27.5 percent year-over-year and San Francisco, Los Angeles and San Diego were up 24.8 percent, 20.8 and 20.4, respectively. 

San Francisco's 24.8 percent jump was its biggest yearly return since March 2001.

Despite the gains, prices are still well below their peak levels.

"Following the increase in mortgage rates beginning last May, applications for mortgages have dropped, suggesting that rising interest rates are affecting housing," Blitzer said. 

"The Fed’s announcement last week that QE3 bond buying will continue for the time being may have only a limited, though favorable, impact on housing."

As of July, average home prices across the United States are back to their spring 2004 levels. 

On a monthly basis prices were up 1.9 percent for the 10-City index and 1.8 percent for the 20-City. 

Chicago (3.2%), Las Vegas (2.8), Detroit (2.7), Tampa (2.3), San Francisco (2.2) and Atlanta (2.2) showed the largest monthly growth. 

Phoenix has posted 22 consecutive months of positive returns. 

A separate report on Tuesday from the Federal Housing Finance Agency showed that prices were up 8.8 percent from July last year and up 1 percent over June, which showed a 0.7 percent increase. 

The index is 9.6 percent below its April 2007 peak.