WASHINGTON (MarketWatch) — Pending home sales climbed 8.2% in May and were another signal of stabilization in a difficult housing market after a dismal April, the National Association of Realtors said Wednesday

The rise in pending home sales, which represent contracts signed on existing homes, comes after an 11.3% downturn in April. The NAR initially had reported that April’s pending home sales declined 11.6%.

The 13.4% gain from May 2010 levels marks the first time in 13 months that contract activity was above year-ago levels.

The S&P/Case-Shiller 20-city home price index rose in April for the first time in eight months, according to data released Tuesday.

“The underlying trend in sales is flat or slightly downwards, but we do not expect a serious further decline,” said Ian Shepherdson, chief U.S. economist at High Frequency Economics. “The combination of rising employment, low mortgage rates, slightly easier financing conditions and reduced fear of capital loss ought to be enough to generate a modest increase in activity by the end of the year.”

NAR Chief Economist Lawrence Yun said that absorption of inventory is the key to price improvement.

Some markets including Hartford, Conn., Houston, Indianapolis, Minneapolis and Seattle have seen a rapid turnaround, with signings up by as much as 30% from year-earlier levels, he added.

Yun repeated a call for banks to return to normal underwriting standards and said a “nonsensical” situation has developed in some states, with the Housing and Urban Development agency unable to complete foreclosure deals because of insufficient funds to pay attorney fees at closing.

Pending home sales historically has closely correlated existing home-sales figures produced by the same trade group. The pending home-sales series has been running more strongly than mortgage applications suggest, due to a greater share of all-cash buyers, according to Michelle Meyer, an economist at Bank of America Merrill Lynch.