GLOBAL MARKETS-Oil posts strong rebound as dollar falls back

* U.S (Other OTC: UBGXF - news) . dollar hits lowest level vs euro since Oct (HKSE: 3366-OL.HK - news)

* Wall St down after weak services data but off lows

* European shares hurt by weak earnings

* Oil bounces 5 pct after U.S. data sparks short-covering

* 10-year Treasury yields fall to 1-year low (Updates with opening of U.S. markets; pvs dateline London)

By Lewis Krauskopf

NEW YORK, Feb 3 (Reuters) - U.S. and European stocks came off their lows on Wednesday, helped by rebounding oil prices, while a soft report on the U.S. services sector weighed on the dollar by making future rate hikes appear less likely.

The U.S. dollar hit its lowest level against the euro since October and wiped out recent gains against the yen. A top Federal Reserve official said the weakening outlook for the global economy and any further strengthening of the dollar could have "significant consequences" for the U.S. economy.

The U.S. economy's service sector expanded in January at a slower pace than the previous month, according to the Institute for Supply Management. Investors had been encouraged earlier in the session by data from a payrolls processor that found U.S. private employers added 205,000 jobs in January, above economists' expectations.

"There is ongoing concern reflected in the market today, and maybe yesterday, about the slowdown in the manufacturing sector spreading to the consumer side of the economy," said Jim Paulsen, chief investment officer at Wells Capital Management in Minneapolis.

The Dow Jones industrial average rose 25.2 points, or 0.16 percent, to 16,178.74, the S&P 500 lost 5.91 points, or 0.31 percent, to 1,897.12 and the Nasdaq Composite dropped 34.63 points, or 0.77 percent, to 4,482.32.

European shares fell as weak earnings from some leading companies weighed.

The pan-European FTSEurofirst 300 index fell 2.1 percent, amid disappointing earnings from Finnish state-controlled utility Fortum (Other OTC: FOJCF - news) and Dutch telecoms group KPN (Amsterdam: KPN.AS - news) .

Data showed euro zone businesses had a disappointing start to 2016, with growth in January matching the worst seen last year.

MSCI (NYSE: MSCI - news) 's 46-country All World share index fell 1 percent.

Equities have been tightly correlated to oil in recent weeks as the commodity's 1-1/2-year slide has deepened, with investors worried that oil's slide is a sign of shakiness in the global economy.

Oil rose after investors took advantage of a drop in the U.S. dollar and earlier weakness in the crude price, despite weekly data showing a surprisingly large rise in U.S. inventory. Russia also repeated its willingness to take part in talks with OPEC producers to cut output.

U.S. crude gained 5.2 percent to $31.42 a barrel, while benchmark Brent crude gained 5 percent to $34.37 a barrel.

Financial conditions have tightened considerably since the Fed raised interest rates and monetary policymakers will have to take that into consideration should that phenomenon persist, William Dudley, president of the Federal Reserve Bank of New (KOSDAQ: 160550.KQ - news) York, told MNI (LSE: 0LYY.L - news) in an interview.

Dudley's comments, combined with the ISM data, raised skepticism about the Fed's ability to further raise rates, weighing on the dollar.

The greenback fell 1.3 percent against a basket of currencies, while the euro gained 1.2 percent against the dollar.

"Fed rate forecasts are coming under fire," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington, in reference to Fed policymakers' December forecast of four rate hikes this year.

U.S. Treasury yields fell to a one-year low after the ISM services data.

Benchmark 10-year note yields were last up 16/32 prices to yield 1.8104 percent, from 1.83 percent overnight. At one point, yields fell below technical resistance to a low of 1.7930 percent, the lowest since February 5, 2015. (Additional reporting by Karen Brettell and Sam Forgione in New York, Nigel Stephenson and Sudip Kar-Gupta in London; Editing by Mark Heinrich)