* China exports fall for 2nd straight month in March
* U.S. crude stocks rise, at record on Gulf Coast - EIA
* Libya oil guards take control of Hariga port, Zueitina pending
* OPEC sees lower demand for its crude in 2014 (Recasts throughout, adds settlement prices)
By Elizabeth Dilts
NEW YORK, April 10 (Reuters) - Global crude oil drifted modestly lower on Thursday, pressured by weaker economic data from China as well as the prospect of a rebound in oil exports from Libya.
Both China's exports and crude imports fell, stoking concerns about demand in the world's second-biggest economy. The trade data coincided with news that OPEC lowered its 2014 forecast for oil demand.
The Libyan government lifted a force majeure on the eastern port of Hariga, which had been blockaded due to a dispute with rebel groups. However, a force majeure remained in effect at Zueitina, the other Libyan port the government recently reopened, making a full rebound in exports uncertain.
Tensions between the West and Russia bubbled in the background as Russian President Vladimir Putin threatened to cut off natural gas supplies to Ukraine if it did not pay its bill.
U.S. crude oil was supported slightly by news that U.S. jobless claims fell to their lowest level in 7 years.
But that was not enough to outweigh data released Wednesday that showed U.S. crude oil stocks jumped by 4 million barrels last week.
"The market was knocked by the Chinese import export data - it was a bearish double whammy," said Matt Smith, analyst at Schneider Electric in Louisville, Kentucky. "But we're loath to move lower given the dual concern of Moscow and Libya, where there is uncertainty as to when control of those ports will transfer power."
Brent settled 52 cents lower at $107.46 a barrel. U.S. crude settled 20 cents down at $103.40 per barrel.
The closely watched and traded Brent-WTI spread CL-LCO1=R tightened 32 to settle at $4.06, its narrowest settlement since Sept. 19.
Further losses in Brent were stemmed by optimism after the U.S. Federal Reserve's dovish policy meeting suggested the central bank may be more cautious toward raising interest rates, easing market concerns of a pullback in stimulus before the economy is ready.
In his most explicit threat to date, President Vladimir Putin warned European leaders Russia would cut natural gas supplies to Ukraine, which could lead to a reduction of onward deliveries to Europe.
The threat risks worsening a dispute with the West over Russia's annexation of Crimea, and investors are watching to see whether it results in stiffer economic sanctions on Moscow.
A steep fall in U.S. gasoline stockpiles also put a floor under oil prices. Gasoline stocks fell by 5.2 million barrels to 210 million barrels in the week ended April 4, Energy Information Administration (EIA) data showed, more than the expected 729,000-barrel draw.