But the Case-Shiller index, a survey that measures prices in 20 metropolitan areas, also reported that the pace of decline had begun to slow in June from May.

A separate report on Tuesday showed that more Americans bought new homes in July, reversing a decline in June.

On an annual basis, prices are plummeting at record levels, according to the Case-Shiller index. In June, home prices in the 20 cities in the index were 15.9 percent below their level in the period a year ago. The 10-city index, which began in 1988, was off 17 percent, its worst annual reading ever.

All 20 cities measured by the index reported year-over-year declines in June. Prices in seven cities are off by more than 20 percent. Las Vegas continued to suffer the worst decline, at a 28.6 percent annual rate, followed by Miami at 28.3 percent, and Phoenix at 27.9 percent.

But there were signs in the report that the pace of the decline in home values slowed in June. For the month alone, nine cities recorded an increase in home values, with values in Boston, Denver and Minneapolis all up at least 1 percent. That compared with seven cities in May.

And the overall decline in June was less than the decline in May.

“While there is no national turnaround in residential real estate prices, it is possible that we are seeing some regions struggling to come back, which has resulted in some moderation in price declines at the national level,” David Blitzer, who supervises the index for Standard & Poor’s, wrote in a news release.

The Case-Shiller index is considered by economists to be the most reliable indicator of American home values. Only previously owned, single-family homes are included in the survey.

For April through June, American home prices were 15.4 percent lower than the second quarter of 2007. That compared with a 14.2 percent annual decline for the first three months of 2008.

The Commerce Department, meanwhile, reported that sales of new homes rose 2.4 percent last month, to a seasonally adjusted annual rate of 515,000. But while homebuilders will welcome the signs of increased demand, sales of new homes were still 35.3 percent below their level in July 2007.

The median price of a new home in July was $230,700.

On Monday, the National Association of Realtors said that sales of previously owned homes rose 3.1 percent last month. But at least a third of those sales came from foreclosed homes, or properties sold by their owner at a loss.

By Michael M. Grynbaum / New York Times News Service