Growth in the U.S. service sector slowed in June as new orders fell and employment contracted, bolstering the view that overall economic growth will moderate in the second half of this year.

Economists said that although the Institute for Supply Management report on the vast U.S. services sector was consistent with a slow down it was still a far cry from the "double-dip" scenario that some investors fear.

U.S. stocks, battered by weeks of declines, continued to enjoy a sharp rebound on Tuesday morning, suggesting investors had more than priced in the data, while safe-haven Treasuries were little changed in a sign the data had not added to fears about the strength of the economy.

"It's consistent with the general tone of data, suggesting that the pace of growth is a little more moderate," said Charles Lieberman, Chief Investment officer at Advisors Capital Management in New Jersey.

"It's certainly not suggestive of the double-dip scenario that some people are pushing."

The Institute for Supply Management said its index of national non-manufacturing or service sector activity fell to 53.8 from 55.4 in May, its slowest pace of growth since February.

The median forecast of 72 economists surveyed by Reuters was for a reading of 55. A reading below 50 indicates contraction in the sector, while a number above 50 means expansion.

The report's employment component fell to 49.7 from 50.4, contracting again after turning positive last month for the first time since December 2007, and confirming recent weak reports on the labor market.

New orders, one of the first components to respond to signs of weakness in the economy, also fell, dropping to 54.4 from 57.1, suggesting growth may be moderating, while export orders turned negative.

The U.S. non-manufacturing sector grew in June for a sixth straight month but the rate of growth slowed more than expected and hit its lowest since February, according to an industry report released Tuesday.