* U.S. crude stocks fell 1.8 mln barrels last week - API
Cushing stocks down 1.5 million barrels - API
* U.S. dollar near eight-week low against euro
* Increased risk of Ukraine civil war supports oil prices
* Coming up: EIA weekly inventory data at 1430 GMT
(Rewrites throughout, updates prices, adds quote, previous dateline SINGAPORE)
By David Sheppard and Julia Fioretti
LONDON, May 7 (Reuters) - Brent crude edged further above $107 a barrel on Wednesday, underpinned by rising tensions in Ukraine, though its premium over U.S. prices narrowed after an industry report showed a sharp draw in inventories in the world's largest oil consumer.
Brent rose 33 cents to $107.39 a barrel by 0816 GMT, after ending the previous session 66 cents lower.
U.S. crude added $1.01 at $100.51 a barrel, on course for its biggest one-day gain since early April. The Brent-WTI spread <CL-LCO1=R> narrowed to $6.88 a barrel, the smallest gap in more than a week.
Crude inventories in the United States fell by 1.8 million barrels last week, the American Petroleum Institute (API) said late on Tuesday, going against analyst expectations for a 1.4-million-barrel gain.
The API said stocks at the Cushing, Oklahoma delivery hub of the U.S. oil futures contract - known as West Texas Intermediate (WTI) - fell by 1.5 million barrels.
"WTI has found some support from the API numbers, the fall in total stocks and also a strong decline in Cushing stocks," Commerzbank analyst Carsten Fritsch said.
"Brent should benefit more from Ukraine," he added, due to its closer proximity to the region and role as the international seaborne benchmark.
Investors are awaiting confirmation of the API numbers from the U.S. government's Energy Information Administration, which releases its more closely watched data later on Wednesday.
The U.S. dollar fell to around an eight-week low against the euro, another bullish factor for U.S. oil and other commodities priced in the dollar as a weak greenback makes them cheaper in terms of other currencies.
RISK OF CIVIL WAR
Heightening tensions in Ukraine and the possibility of the country slipping into civil war also helped lift oil markets, as traders weighed the risk of supply disruptions from Russia, the world's second-largest oil exporter.
Peace efforts in Ukraine seemed less likely as both supporters of Russia and of a united Ukraine accused each other of tearing the country apart, as violence spread to the eastern port of Mariupol.
The Obama administration is working on new sanctions to impose on Russia if it ramps up aggression against Ukraine, such as preventing elections from taking place in much of the country or recognising another separatist referendum, U.S. officials said on Tuesday.
While gas and oil supplies have not been significantly disrupted by the Ukraine situation so far, traders and analysts say the risk remains that the United States and European Union could target the Russian energy industry, or Moscow could choose to restrict exports.
(Additional reporting by Jacob Gronholt-Pedersen in Singapore; Editing by Dale Hudson)