* U.S. equities recoup earlier losses, supporting oil
* Chinese factory activity shrinks, raising demand doubts
* U.S. single-family home sales rise 2.3 pct
* Euro zone business downturn eases in May-PMI
* U.S. gasoline stocks abundant ahead of driving season (Updates prices, recasts)
By Anna Louie Sussman
NEW YORK, May 23 (Reuters) - Brent crude oil prices retraced earlier losses after falling to a three-week low on Thursday in a broader commodities selloff, riding the coattails of a late turnaround in U.S. equities to end flat.
Traders said the U.S. equity market's steady recovery from earlier lows supported oil prices, which moved largely in tandem with the stock markets.
They also cited U.S. crude's failure to break through its 200-day moving average, a technical support level. After briefly trading slightly below it, U.S. crude began climbing back up and never looked back, and Brent crude prices rose in lockstep.
Brent crude settled down 16 cents to $102.44 a barrel, recouping losses of nearly $2 after earlier reaching $100.64, its lowest price since May 2. Prices are still down sharply from a 2013 high of $119.17 reached on Feb. 8.
U.S. crude ended nearly flat, down 3 cents to $94.25 and even briefly going positive in post-settlement trading. It had earlier lost more than $2 in intra-day trading.
"Equities are holding in pretty well, and the market's in an uptrend with equities, but nothing else has fundamentally changed," said Bill Baruch, senior market strategist at iitrader.com in Chicago, Illinois.
"There's a large short position in the market and the funds are covering positions before the holiday weekend," he added, referring to the forthcoming Memorial Day holiday in the United States.
A decline in China's factory activity had entrenched concern about weak demand in the world's second-largest oil consumer, weighing on prices in early trading.
Oil prices bottomed out around 10 a.m. EDT (1400 GMT) after the release of strong U.S. housing data stoked worries about a tapering of U.S. Federal Reserve stimulus, sending equity markets down.
"It's a pretty volatile session. We bounced back and are following the equity markets a bit," said Addison Armstrong, director of market research at Tradition Energy in Stamford, Connecticut.
China's factory activity shrank for the first time in seven months in May, a survey showed, weighing on oil as well as copper, for which China is the world's top consumer.
Sales of new U.S. single-family homes rose 2.3 percent in April, and prices climbed to record high levels, offering strong proof the sector's rebound trend is intact.
While signs of economic recovery would ordinarily be supportive for oil, market-watchers are interpreting news in light of how it may affect the U.S. Federal Reserve's quantitative easing policies that have pumped hundreds of billions of dollars into money markets, boosting many commodities, including oil.
"You can't please these guys. Now every time we get data that's good, it suggests we'll get a tapering off the stimulus," said Phil Flynn, analyst at Price Futures Group in Chicago, Illinois.
"So when we see housing data that blows away expectations, it makes us pull back a bit."
Fed Chairman Ben Bernanke told a congressional committee on Wednesday the Fed could scale back the pace of bond purchases at one of its next few policy meetings.
Euro zone data on Thursday offered little support for oil prices. While a downturn eased slightly this month, a dearth of new orders means the region's economy is likely to contract again in the second quarter, surveys showed.
Oil also fell on Wednesday pressured by a rise in U.S. gasoline inventories.
A weekly U.S. Energy Information Administration report showed gasoline stocks are close to their highest level for the time of year since 1999, indicating ample supply for the summer driving season when demand rises. (Additional reporting by Robert Gibbons in New York, Alex Lawler in London and Ramya Venugopal in Chennai; Editing by Marguerita Choy, Alden Bentley and Andrew Hay)