By Sam Forgione

NEW YORK (Reuters) - U.S. and European shares fell on Wednesday as a drop in oil prices weighed on energy stocks, while two-year U.S. Treasury yields were on track for their biggest monthly increase since December on growing expectations for a Federal Reserve rate hike.

Oil prices tumbled to more than two-week lows, with U.S. crude falling more than 3.5 percent, after government data showed a large weekly build in U.S. crude and distillate stockpiles and a smaller-than-expected draw in gasoline.

The weakness in oil prices fueled losses in the S&P energy index <.SPNY>, which was last down 1.8 percent, and the European STOXX 600 Oil and Gas sector <.SXEP>, which closed down 1.4 percent.

Investors remained focused, however, on U.S. non-farm payrolls data due on Friday, which could provide clues on the timing of the next Fed rate increase.

Boston Fed president Eric Rosengren said the U.S. central bank was nearing its employment and inflation rate goals, adding that rate hikes could shield the economy from risks.

Data showing the U.S. private sector added 177,000 jobs in August, compared with expectations of 175,000, boosted investors' optimism about Friday's jobs report. Analysts have noted low trading volumes in recent days, partly on anticipation of the jobs data.

"Today will be very quiet," said John Brady, senior vice president at R.J. O'Brien & Associates in Chicago. "It's late August and most risk managers aren't going to allow traders to comes in with large positions."

Yields on U.S. two-year Treasuries <US2YT=RR>, which are more sensitive than longer-dated maturities to expectations about the timing of Fed rate increases, were set to post an increase of more than 12 basis points for August.

That monthly rise would be their biggest since last December, when the Fed raised rates for the first time in nearly a decade. A chorus of Fed officials saying that rate hikes look appropriate before year-end has increased expectations for higher short-term rates.

Benchmark 10-year Treasury <US10YT=RR> yields were set to post their biggest monthly increase in more than a year, of more than 10 basis points.

MSCI's all-country world equity index <.MIWD00000PUS> was last down 1.63 points, or 0.39 percent, at 416.14.

The Dow Jones industrial average <.DJI> was last down 83.45 points, or 0.45 percent, at 18,370.85. The S&P 500 <.SPX> was down 10.44 points, or 0.48 percent, at 2,165.68. The Nasdaq Composite <.IXIC> was down 18.82 points, or 0.36 percent, at 5,204.17.

Europe's broad FTSEurofirst 300 index <.FTEU3> closed down 0.36 percent, at 1,352.28.

Brent crude <LCOc1> was last down $1.34, or 2.77 percent, at $47.03 a barrel. U.S. crude <CLc1> was last down $1.73, or 3.73 percent, at $44.62 per barrel.

The U.S. dollar index, which measures the greenback against a basket of six major rivals, hit a three-week high of 96.255 after the slightly stronger-than-expected U.S. ADP data, but pared gains on weak manufacturing data.

“For the time being, the narrative is pretty dollar bullish," said Richard Franulovich, a senior currency strategist at Westpac Banking Corporation in New York.

Spot gold slid to a two-month low of $1,304.91 an ounce after the U.S. private payrolls data.

(Additional reporting by Jamie McGeever in London, Dion Rabouin and Karen Brettell in New York, and Yashaswini Swamynathan in Bengaluru; Editing by Nick Zieminski and Meredith Mazzilli)