* U.S. crude stocks fell 1.8 mln barrels last week - EIA
* Cushing stocks down 1.4 million barrels - EIA
* Libyan rebels occupying ports refuse to deal with new PM
* Putin calls for separatists to postpone referendum
(Rewrites first paragraph, adds settlement prices, analyst commentary)
NEW YORK, May 7 (Reuters) - Global oil prices rose by more than $1 a barrel on both sides of the Atlantic on Wednesday as an unexpected drop in United States inventories supported U.S. crude and escalating tensions in Libya pushed Brent higher.
The U.S. Energy Information Administration said U.S. crude inventories fell 1.8 million barrels last week, compared with analyst' forecasts for a 1.4-million-barrel build. Stocks fell 1.4 million barrels at the Cushing, Oklahoma, delivery point of the U.S. futures contract, to their lowest since 2008.
Libyan rebels occupying oil ports in the east of the country said they would not deal with new Prime Minister Ahmed Maiteeq, despite an agreement with Maiteeq's predecessor last month to reopen four ports.
Protests at Libya's major oilfields and ports have decimated its oil production to just over 250,000 barrels per day from around 1.4 million bpd in mid-2013 and slowed exports to a trickle.
U.S. crude settled $1.27 higher at $100.77 a barrel. Brent crude settled up $1.07 at $108.13 a barrel.
Also supportive for global oil prices, U.S. gasoline settled more than 3 cents higher at $2.9182 a gallon.
"There are underlying bullish factors here," said Carl Larry, chief executive of consultancy Oil Outlooks. "(Seasonally) refiners are at that turning point where we're out of maintenance and coming back to refinery production."
Brent was pressured after Russian President Vladimir Putin said he was ready to discuss a way out of the Ukrainian crisis and called on separatists in east Ukraine to postpone a May 11 referendum on the status of the mostly Russian-speaking region.
He spoke after talks with the head of the Organization for Security and Cooperation in Europe, who said the security and rights body would soon propose a "road map" to defuse the crisis.
While gas and oil supplies have not been significantly disrupted by the Ukraine situation, traders and analysts say the risk remains that the United States and European Union could target the Russian energy industry with sanctions, or Moscow could choose to restrict exports.
"If President Putin is serious about defusing the Ukraine crisis, oil prices should come under considerable pressure, as the security premium has been inflated over the situation and the supply that hangs in the balance," said John Kilduff, a partner at Again Capital in New York.
"Unfortunately, recent history suggests that is another round of wishful, if not un-serious, rhetoric, with no real change in Russia's position afoot."
European governments reached a preliminary agreement that would make it easier for the EU to target Russian companies with sanctions as a method of pressuring Russia over Ukraine.
Unrest also hit oil infrastructure in Yemen where assailants blew up its main oil export pipeline, halting crude flows.
(Additional reporting by Robert Gibbons and Anna Louie Sussman in New York, David Sheppard and Julia Fioretti in London, and Jacob Gronholt-Pedersen in Singapore; Editing by William Hardy and Marguerita Choy)