* Ukraine tense as new leader says no talks with "terrorists" * Libya oil output 160,000 bpd vs 1.4 million bpd before uprising * Eastern Libya rebel rejects new government, blockade continues * Iran: big powers want "too much" in nuclear talks * Coming Up: U.S. Dallas Fed Manufacturing Index at 1430 GMT (Updates prices, adds detail, comment) By Christopher Johnson LONDON, May 27 (Reuters) - Brent crude oil steadied just below $110 a barrel on Tuesday on supply worries as the Ukraine government launched air strikes to try to put down a separatist revolt and Libya struggled to rein in rebels controlling several of the country's oil ports. Brent was down 50 cents at $109.82 a barrel by 1010 GMT, not far below last Thursday's intraday peak of $111.04, its highest for more than two and a half months. U.S. light crude oil was down 30 cents at $104.05. Ukrainian forces fought separatists in Donetsk for a second day on Tuesday after inflicting heavy losses on the rebels, with the government vowing to press on with a military offensive "until not a single terrorist" is left. Ukraine is a main gas supply route to Europe from Russia and investors are concerned the conflict could also disrupt Russian oil supplies to the West. Chaos in Libya, meanwhile, has cut the country's oil output to only 160,000 barrels per day (bpd), compared with 1.4 million bpd before the 2011 uprising against Muammar Gaddafi. "The market is worried about what is happening in Ukraine, where the crisis appears to escalating, and the muddy supply picture in Libya is also underpinning prices," said Carsten Fritsch, senior oil and commodities analyst at Commerzbank. "The risk for prices is to the upside from here," he added. Heightened political risks have helped Brent to gain more than 6 percent since this year's low of $103.95 in early April. In Libya, the leader of protesters occupying the country's oil ports said he did not recognise Prime Minister Ahmed Maiteeq's new government and indicated that a previously agreed deal to end his blockade could be in jeopardy. Oil, particularly Brent, also drew support from hopes of demand growth amid expectations that the European Central Bank (ECB) is preparing a package of policy options to help to stimulate the euro zone economy. Progress of talks between Iran and world powers to find a solution to Tehran's nuclear programme is also being watched by investors. Iran said world powers were demanding too much in talks aimed at reaching a deal by July 20 but maintained that hurdles could be overcome. Investors also awaited a slew of economic indicators from the United States and Europe to gauge the demand outlook. U.S. durable goods orders, consumer confidence and the Dallas Fed manufacturing index are due on Tuesday. (Additional reporting by Manash Goswami in Singapore; Editing by Jason Neely and David Goodman)

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