* U.S. shares seesaw between gains and losses
* China factory activity contracts, stoking economic fears
* 10-year Treasury notes and safe-haven yen rally (Updates to mid-afternoon in U.S. markets)
By April Joyner
NEW YORK, Jan 2 (Reuters) - Stocks recovered much of their losses on Wednesday as investors took advantage of cheaper shares to ring in the new year, but lingering economic concerns from weak Chinese and European data boosted safe-haven assets including benchmark U.S. Treasury notes and the Japanese yen.
Data showed Chinese factory activity contracting for the first time in more than two years. The Purchasing Managers' Index (PMI) for the euro zone also reached its lowest level since February 2016, and France's PMI fell in December for the first time in two years. Concerns about the flagging global economy contributed to U.S. stocks posting a loss in 2018 for the first time in a decade.
The U.S. benchmark S&P 500 stock index dropped as much as 1.6 percent on the data but moved higher to fluctuate between positive and negative territory as the session continued. Bank and energy shares, which have been especially hard-hit in recent sell-offs, were among the biggest gainers.
Energy shares also benefited from a jump in oil prices, which climbed as U.S. stocks recovered.
"We're at levels that are really, really oversold, and that's where bounces really come from," said Michael Antonelli, managing director of institutional sales trading at Robert W. Baird in Milwaukee. "Slowing China growth isn't anything new, and that's what led to today's bounce."
Still, MSCI's gauge of stocks around the globe dropped 0.45 percent. Asian markets as well as the pan-European STOXX 600 closed lower.
Reflecting lingering investor nervousness, yields on U.S. 10-year Treasury notes fell, earlier hitting an 11-month low. However, the boost in oil prices pushed up yields on short-dated maturities, flattening the yield curve . An inverted yield curve is widely seen as an indicator of a future recession.
"The yield curve is signaling that something is wrong," said Matt Miskin, market strategist at John Hancock Investments in Boston. "The underlying economic data continues to suggest a slowdown."
The safe-haven Japanese yen also rose to reach a seven-month high against the dollar.
Yet the dollar index, which measures the greenback against a basket of six other currencies, advanced 0.7 percent as the euro and sterling fell.
The Dow Jones Industrial Average fell 98.22 points, or 0.42 percent, to 23,229.24, the S&P 500 lost 5.61 points, or 0.22 percent, to 2,501.24 and the Nasdaq Composite added 9.85 points, or 0.15 percent, to 6,645.13.
Benchmark 10-year U.S. Treasury notes last rose 10/32 in price to yield 2.6557 percent, from 2.691 percent late on Monday.
Brent crude futures gained $1.11, or 2.06 percent, to settle at $54.91 a barrel. U.S. crude futures rose $1.13, or 2.49 percent, to settle at $46.54 a barrel.
Reporting by April Joyner; Additional reporting by Wayne Cole in Sydney and Sujata Rao and Abhinav Ramnarayan in London; Editing by Andrea Ricci and Lisa Shumaker