* NATO warns of "grave consequences" if Russia moves into Ukraine * Libya's preparations to load crude cap gains (Recasts, updates throughout, changes dateline from SINGAPORE) By Ron Bousso LONDON, April 8 (Reuters) - Brent crude rose above $106 a barrel on Tuesday as fresh unrest in eastern Ukraine heightened tension between Russia and the West, but hopes Libya would soon resume oil exports kept prices capped. The gains came amid a broad retreat in global equity markets recently and a weakening of the dollar, with investors turning to oil for exposure to global economic growth. Brent crude for May delivery was up 63 cents at $106.45 a barrel by 0933 GMT. U.S. crude for May rose 85 cents to $101.29 a barrel. "The geopolitical risk is increasing with increasing tension between Russia and Ukraine," said Bjarne Schieldrop, chief commodities analyst for Norway-based SEB. Ukrainian police detained 70 pro-Moscow protesters occupying a government building in the Russian-speaking industrial heartland in the east of the country overnight as Kiev accused Russia of seeking to dismember the country. NATO Secretary-General Anders Fogh Rasmussen warned Moscow that if it were to encroach into eastern Ukraine there would be "grave consequences" for its relationship with the alliance. Russia is the world's biggest oil producer, and any deep diplomatic rift between Moscow and the West worries investors. Crude prices dropped on Monday and remained under pressure on Tuesday due to the prospect of additional Libyan supplies after rebels agreed to end gradually their eight-month blockade of oil ports accounting for around 700,000 barrels per day. "Hiccups can still develop on the way to a full return of supplies from Libya but this is nonetheless a bearish development," said Oliver Jakob, an analyst at Switzerland-based Petromatrix. IRAN TALKS The bearish tone for oil was also underpinned by an easing of tensions between the West and Iran. Tehran said it hopes enough progress will be made this week to enable negotiators to start drafting by mid-May a final accord to settle a long-running dispute over its nuclear programme. The Islamic Republic and six world powers will hold a new round of talks in Vienna on Tuesday and Wednesday. "If the current round of discussion in Vienna confirms that the final agreement will be drafted in May ... then the market will again start to focus a bit more on the supply and demand for the second half of the year including higher flows of Iranian crude oil, in an environment where Iraq is also increasing production," Jakob said. U.S. oil stocks were expected to have risen last week, a preliminary Reuters poll of four analysts showed ahead of a weekly inventory report from industry group the American Petroleum Institute. (Editing by Dale Hudson)

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