NEW YORK (Reuters) - U.S. single-family home prices rose in June though the pace of gains slowed slightly, a closely watched survey showed on Tuesday.

The S&P/Case Shiller composite index of 20 metropolitan areas rose 0.9 percent on a seasonally adjusted basis, just shy of economists' forecast for a 1 percent increase. Prices rose 1 percent in May.

On a non-adjusted basis, prices rose 2.2 percent.

Compared to a year earlier, prices were up 12.1 percent, in line with economists' expectations. Prices were up 12.2 percent in the year to May, the biggest gain in more than seven years.

The report suggested the housing sector continues to recover, making it a bright spot in the broader U.S. economic rebound.

Prices in all 20 cities rose on a yearly basis, led by a 24.9 percent surge in Las Vegas followed closely by a 24.5 percent gain in San Francisco.

Only in six cities, however, did prices rise in June at a faster clip than in the previous month, down from 10 in May.

"Overall the report shows that housing prices are rising but the pace may be slowing," David Blitzer, chairman of the index committee at S&P Dow Jones Indices, said in a statement.

"With interest rates rising to almost 4.6 percent, home buyers may be discouraged and sharp increases may be dampened."

Borrowing costs are up more than a percentage point since May in anticipation that the Federal Reserve will begin pulling back on support for the economy by purchasing fewer bonds. Its monthly purchases had been keeping long-term interest rates low.

Other housing data has suggested higher mortgage rates are slowing refinancing activity and possibly the pace of sales. Data last week revealed sales of new single-family homes fell 13 percent in July to their lowest level in nine months.

"Other housing news is positive, but not as robust as last spring," Blitzer said.

Still, rates remain low by historical standards and most economists do not expect the higher costs to end the recovery altogether. In the short-term, it could also spur potential buyers to act before rates rise further.

On a quarterly basis, prices were up 7.1 percent between April and June and 10.1 percent over the last four quarters, the S&P/Case-Shiller data showed.

(Reporting By Steven C. Johnson; Editing by Chizu Nomiyama)