U.S. home prices rose in May for the first time in three years, suggesting the housing market is stabilizing, but a weakening job market hit consumer confidence in July and could prevent near-term economic recovery.

Potential home buyers afraid of committing to a fast depreciating asset have been clamoring for such signs of house price stabilization.

But rising unemployment and wage cuts are straining consumer optimism and keeping many potential buyers out of the housing market, impeding spending and prospects for economic rebound.

People are getting a bit discouraged. Jobs are not coming as quickly as expected, said John Silvia, chief economist at Wells Fargo in Charlotte, North Carolina. This won't be a V-shaped recovery for either the economy or the jobs market.

Home prices have plunged more than 32 percent on average from their 2006 peaks, but the pace of the annual declines slowed in May for the fourth straight month, according to Standard & Poor's/Case Shiller home price indexes on Tuesday.

This could be an indication that home price declines are finally stabilizing after tumbling to 2003 levels, David M. Blitzer, chairman of the index committee at S&P, said in a statement.

The index of 20 metropolitan areas rose 0.5 percent in May from April, after a 0.6 percent drop the month before, in contrast with the 0.5 percent drop forecast in a Reuters poll.

The pressures are all working in alignment to support that we're at the turning point in the worst housing market since the Great Depression, said Steve Hagenbuckle, managing principle for TerraCap Partners, a distressed real estate private equity fund in Cape Coral, Florida,

Affordability is at all time highs, inventories are shrinking, there's competition for properties, and we're not building as much new product to compete with the existing homes, he said.

Still, caution is warranted as long as the U.S. unemployment rate keeps rising, economists advised. That rate is at its highest in nearly 26 years and is headed to double-digit levels.

For a rebound, consumer confidence needs to improve, foreclosures need to start falling from their record pace and potential buyers need to have a sense that it won't be even cheaper to purchase if they keep waiting.

Consumer confidence, however, fell more than expected this month because of the worsening job market.

The U.S. Conference Board's index of consumer sentiment fell to 46.6 in July from 49.3 in June, according to data published on Tuesday. A reading of 49 was forecast in a Reuters survey.

The eroding sentiment came as Americans saying jobs are hard to get increased and those who thought jobs were plentiful fell to its lowest in more than a quarter century.

Consumers are feeling no love in this recovery, said Boris Schlossberg, director of foreign exchange research at GFT in New York. Consumers are still concerned about the labor market and their own security.

(Additional reporting by Richard Leong, Gertrude Chavez-Dreyfuss and Burton Frierson)