* U.S. accuses Russian agents of stirring eastern Ukraine unrest
* U.S. crude stocks rise 7.1 mln bbls, six-fold higher than forecast -API
* EIA raises 2014 world oil demand growth forecast
* Libya not in full control of re-opened eastern port
SINGAPORE, April 9 (Reuters) - Brent futures held near $108 a barrel as geopolitical tensions over Ukraine worsened, overshadowing U.S. industry data that showed crude stockpiles in the world's largest oil consumer rose nearly six times more than expected.
U.S. Secretary of State John Kerry accused Russian agents and special forces of stirring separatist unrest in eastern Ukraine. Unrest in the region won't directly impact global oil supplies and trade, but overall risk premiums are rising as investors worry that simmering tensions between world powers and Russia could quickly take a turn for the worse.
"Tensions between the West and Russia could lead to unexpected consequences and that's what the market is worried about," said Victor Shum, vice-president of energy consultancy IHS Energy Insight. "But prices are overheated at this point and I do see them on an easing trend, but only moderately."
Brent crude fell 3 cents to $107.64 a barrel by 0332 GMT, after ending $1.85 higher at its highest close in more than a week.
U.S. oil came under pressure from the inventory data and slid 24 cents at $102.32. Both the benchmarks gained the most in five weeks overnight.
Brent could slide to around $106 a barrel, especially after the overnight steep surge, Shum said, adding that the benchmark will average about $8 more than its U.S. counterpart.
Armed pro-Moscow protesters occupied Ukrainian government buildings in two cities in the largely Russian-speaking east. Ukraine says the occupations that began on Sunday are part of a Russian-led plan, and the U.S. said Moscow could be trying to prepare for military action as it had in Crimea.
Investors are also watching developments in Libya and the progress in the country's plan to ramp up exports. Libya's oil protection force is not in full control of the Zueitina port even after a deal with rebels to end the blockade of eastern oil terminals, as some militiamen are still at the facility.
The port, along with the country's two largest, Es Sider and Ras Lanuf, has been under the control of an eastern federalist group led by former guard member Ibrahim al-Jathran, who recruited men from within his ranks.
Prices are drawing additional support from expectations of better demand. The U.S. Energy Information Administration (EIA) raised its 2014 world oil demand growth forecast by 10,000 barrels per day to 1.23 million bpd. But the agency, in its monthly forecast, cut its oil demand growth estimate for 2015 by 10,000 bpd to 1.36 million bpd.
U.S. crude inventories rose by 7.1 million barrels in the week to April 4, data from industry group the American Petroleum Institute showed, compared with analysts' expectations for an increase of 1.3 million barrels.
Crude stocks at the Cushing, Oklahoma, delivery hub rose by 204,000 barrels, API said.
But a steeper-than-expected fall in gasoline stocks is setting a floor under the U.S. oil benchmark as the drawdown is adding to evidence of a broad economic recovery and robust demand as summer driving season gets underway.
U.S. gasoline stocks fell by 3.6 million barrels, compared with expectations of a 700,000-barrel decline.
Investors are awaiting data from the EIA due later in the day as a further gauge of the country's demand outlook.
(Editing by Tom Hogue)