* Cushing stocks fall by 1.53 mln barrels -EIA
* Libyan output at 155,000 barrels per day -official
* Russia, Ukraine, EU hold talks Fri on gas price dispute
(Rewrites first 6 paragraphs, updates with settlement prices, adds analyst commentary)
NEW YORK, May 29 (Reuters) - U.S. crude prices rose on Thursday after government inventory data showed a sharp drawdown in gasoline that outweighed a build in overall crude stocks, while Brent edged up supported by the low Libyan output and the Ukraine crisis.
U.S. crude stockpiles rose 1.7 million barrels last week, but a strong start to the summer driving season drained gasoline inventories by 1.8 million barrels, far more than forecast, the Energy Information Administration reported.
Stockpiles at the Cushing, Oklahoma hub for U.S. crude also fell 1.53 million barrels, EIA said, as shippers continued to flood the Gulf Coast with supplies. Gulf Coast stocks rose 3.1 million barrels, the EIA data showed.
The brighter demand outlook underpinned prices already boosted by concerns about Libyan supply and tensions between the West and Russia, which has threatened to cut off Ukraine's natural gas supply by Monday if a price dispute is not settled.
The U.S. economy contracted for the first time in three years in the first quarter as it buckled under a severe winter, capping crude futures.
U.S. crude oil rose as much as $1.22 to an intra-day high of $103.94 before giving back some gains to settle 86 cents higher at $103.58 a barrel.
Brent crude settled 16 cents higher at $109.97 a barrel after losing 21 cents on Wednesday.
Oil prices have range bound throughout May, with U.S. crude unable to top $105 or fall much below $99 a barrel, while Brent has traded roughly between $111 and just below $107 a barrel.
"The GDP is a little bit weaker, and even though the winter is long gone, people are going to look at the data," said Carl Larry, president of oil consultancy Oil Outlooks. "The market is tired. Whether it's to the upside or downside, there is not much follow through. People are re-focusing on the bigger picture."
Traders continued to watch the situation in Ukraine, where pro-Russian separatists shot down an army helicopter on Thursday, as government forces pressed ahead with an offensive to crush rebellions in the east following the election of a new president.
Talks between Russia, Ukraine and the European Commission are scheduled for Friday, as time runs out to solve a gas price dispute before next Monday, when Moscow has threatened it would cut off supplies.
In Libya, acting prime minister, Abdullah Al-Thinni, refused to hand over power to a newly elected premier after questioning his legitimacy in a deepening confrontation among the OPEC nation's rival factions.
Oil output in the North African country has dropped to just 155,000 barrels per day, just one tenth of capacity, amid the current political crisis.
(Additional reporting by Catherine Ngai, Anna Sussman and Robert Gibbons in New York, David Sheppard in London, and Manash Goswami in Singapore; Editing by Keiron Henderson, Pravin Char, Tom Brown and Marguerita Choy)