By Barani Krishnan

NEW YORK (Reuters) - Oil prices seesawed in volatile trading on Wednesday, barely hanging onto a third day of gains after government data showing a large U.S. crude inventory build surprised traders the morning after an industry group had reported a draw.

The U.S. Energy Information Administration (EIA) said domestic crude inventories rose 3.1 million barrels last week, more than the 2.2 million-barrel build that analysts had forecast in a Reuters survey.

Just on Tuesday preliminary inventory data by the American Petroleum Institute had suggested a drawdown of 1.2 million barrels. [API/S] Oil prices slid after the EIA report.

Brent (LCOc1), the global crude benchmark, was down 24 cents at $51.68 a barrel by 2:22 p.m. EDT (1822 GMT). At its session high, Brent was up more than $1; then it turned negative before edging slightly higher.

The West Texas Intermediate (WTI) benchmark for U.S. crude (CLc1) was down 40 cents at $48.13 a barrel. It had also moved between negative territory and gain of more than $1 at the session high.

In the past three days, Brent and U.S. crude prices had rallied about $4 each, breaking above a month-long trading range on technical buying and supportive data.

The crude build "will take some of the wind out of the market's sails", said Gene McGillian, senior analyst at Tradition Energy in Stamford, Connecticut.

"The report is bearish enough to break the back of the rally," he said. It's cold water on the market."

Tariq Zahir, trader in crude oil spreads at Tyche Capital Advisors in Laurel Hollow in New York, agreed.

"Overall, we have a real battle going on, with crude technically having broken out of the range we have been in for more than a month. $50 for WTI is in sight," Zahir said. "But fundamentally we are seeing builds and that should continue in the weeks to come."

He cited the impending arrival of Iranian oil as nuclear-related sanctions against Tehran come off, and an Atlantic hurricane season that has so far done no damage to U.S. oil installations.

On Tuesday, a monthly report by the EIA projected that global oil demand for 2016 will grow by the fastest rate in six years, suggesting a crude surplus was easing more quickly than expected.

Robin Bieber, director of London brokerage PVM Oil Associates, said the overall trend for oil prices would still be higher.

"The key technical indicators are positive," Bieber said. "It is not advised to be short."

(Additional reporting by Christopher Johnson in London and Aaron Sheldrick in Tokyo; Editing by David Evans, Diane Craft, David Gregorio and Richard Chang)