* Global stocks, Brent buoyed by steps to safeguard banks
* U.S. private sector jobs report also lifts optimism
* Euro falls vs dollar on doubts about Greek progress
* Euro zone private sector activity contracts, a bad sign (Adds opening of U.S. markets, byline, dateline; previous LONDON)
By Herbert Lash
NEW YORK, Oct 5 (Reuters) - Global stocks and oil prices rebounded on Wednesday after reassuring U.S. economic data and hopeful signs authorities are moving forward to contain the latest outbreak in Europe's debt crisis.
Wall Street traded near break-even after opening lower as a better-than-expected report on the U.S. services sector helped offset lingering doubts the debt crisis is over and concerns that data in Europe suggested the region is sliding into recession.
European stocks gained 2 percent, pushed higher by banking shares, and Brent crude bounced back above $101 a barrel on news that European finance ministers are exploring ways to recapitalize the ailing sector. For details see: [ID:nL5E7L51RH] [ID:nL3E7L42VF]
European shares rose after tumbling nearly 5 percent the past three sessions. The benchmark S&P 500 index in the United States had fallen 10 percent over the past six sessions.
The FTSEurofirst 300 <.FTEU3> index of top European shares was up 2.4 percent at 909.45 points. MSCI's all-country world index <.MIWD00000PU> rose 0.8 percent to 274.24.
Brent crude
Surveys that showed private sector business activity shrank in the euro zone for the first time in two years last month as new orders dried up kept enthusiasm among many investors in check.
"I'm not sure this is the end of the bear trend, this is a short term bounce. But until there is actual doing as well as comments, we won't see a sustainable recovery," said Andy Sommer, an analyst at EGL in Dietikon, Switzerland.
The Dow Jones industrial average <.DJI> was up 9.35 points, or 0.09 percent, at 10,818.06. The Standard & Poor's 500 Index <.SPX> was up 2.11 points, or 0.19 percent, at 1,126.06. The Nasdaq Composite Index <.IXIC> was up 2.38 points, or 0.10 percent, at 2,407.20.
The Institute for Supply Management said its services index dipped to 53.0 last month from 53.3 in August but employment in the vast U.S. services sector fell in September to its lowest level since April 2010.
"Beneath the surface, it's actually a fairly mixed report," said Tom Porcelli, chief economist at RBC Capital Markets in New York. "New orders index improved -- it's the best we've seen since the middle of the year -- but the employment index slipped below breakeven."
The euro fell, weighed by a lack of concrete details to deal with the region's debt crisis and worries over a Greek default even after a pledge by policymakers to strengthen European banks. [ID:nN1E7940BT]
A downgrade of Italian sovereign debt by ratings agency
Moody's highlighted the funding difficulties facing the euro
zone's third biggest economy, while France and Belgium were
forced to help Dexia SA
The euro rallied to trade little changed against the dollar after better-than-expected U.S. private-sector jobs data boosted risk appetite but that advance proved fleeting. For the ADP report, click [ID:nEAPA50EH0].
"Slightly better employment data would signal risk preference but a lack of progress in any meaningful way on resolving Greece and the debt crisis in general is keeping risk at bay," said John McCarthy, director of foreign exchange at ING Capital Markets in New York. "A downgrade of Italy has brought everyone back to reality."
The euro
The prices of U.S. Treasury securities fell, with yields nearing session highs after the report on U.S. private sector jobs showed more job growth than expected in September.
Benchmark 10-year Treasury notes