The plunge in U.S. home prices showed signs of leveling off in April, but worries about unemployment pushed consumer confidence to a seven-month low in June.

House prices were helped by the start of the spring selling season, data showed on Tuesday.

Nonetheless, economists warned prices will likely crawl along at low levels as a large number of homes, many of them at bargain prices, come up for sale.

The degree of hemorrhaging seems to be slowing, said Anthony Chan, chief economist at JPMorgan Private Wealth Management in New York.

The patient is still bleeding and will be bleeding until we get all that distressed and shadow housing market inventory down to smaller levels.

Housing accounts for a fraction of the U.S. gross domestic product, and a three-year slump in prices wiped out trillions of dollars in homeowner equity. But a recovery in prices remains key to restoring confidence among consumers.

Consumers were more pessimistic about the economic outlook in June because of worries about the labor market and income prospects.

The Conference Board, a private-sector industry group, said its index of consumer attitudes fell to 58.5 in June from a revised 61.7 in May, and short of expectations for 60.5.

Respondents who said jobs were plentiful slipped to 5.2 percent from 5.7 percent the month before, while the jobs hard to get measure rose to 43.8 percent from 43.5 percent.

The U.S. economy added just 54,000 jobs last month, and data earlier this week showed consumer spending was flat in May from April.

The weaker pace of economic growth in the first quarter persisted into the second quarter, though economists still expect growth to pick up in the second half of 2011 as temporary factors such as high energy prices and supply chain disruptions from Japan's March earthquake ease.

Forecasters see second-quarter growth at around 2 percent after the economy grew at a 1.9 percent pace in the first three months of the year.

The S&P/Case-Shiller composite index of single-family home prices in 20 metropolitan areas dipped 0.1 percent month-over-month on a seasonally adjusted basis. A Reuters poll of economists had forecast a decline of 0.2 percent.

The decline was the smallest since July 2010. Average home prices fell 3.9 percent from a year ago and were still at levels seen in the summer of 2003.

On a non-seasonally adjusted basis, however, the index rose 0.7 percent, its first advance in eight months, the report said.

The seasonally adjusted numbers show that much of the improvement reflects the beginning of the spring-summer home buying season, David Blitzer, chairman of the index committee at Standard & Poor's, said in a statement.

It is much too early to tell if this is a turning point or simply due to some warmer weather.

Prices were supported last spring by a tax credit, but the housing market has struggled since the credit expired.

A monthly increase in prices in nine of the 20 cities in the index suggests some of the more severe pressure in the wake of the expiration has waned, Barclays Capital Research said.

The housing report helped give U.S. stocks a boost, as did optimism the Greek parliament would adopt an unpopular austerity plan needed to avert the euro zone's first default.

The Conference Board report echoed the preliminary Thomson Reuters/University of Michigan survey earlier in the month.

Economists said issues including wrangling in Washington over the debt ceiling and the lack of immediate policy options to boost the economy further also probably hurt consumer sentiment.

Add turmoil abroad, a debt ceiling commission still in gridlock and a Federal Reserve that appears to have emptied out their bag of tricks, and it's no wonder the consumer has lost confidence in the recovery, Lindsey Piegza, economist at FTN Financial, wrote in a note.

In a positive sign, data from the Richmond Federal Reserve showed regional manufacturing growth firmed again with the composite index coming in at 3 in June from minus 6 the month before.

The regional indicator comes ahead of the larger national manufacturing figure from the Institute for Supply Management on Friday, which is expected to show the pace of manufacturing growth slowed again in June.

(Additional reporting by Alexandra Alper; Editing by Padraic Cassidy)

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