* U.S. crude oil settles more than $2 higher
* U.S. crude oil stocks seen rising 1.3 mln barrels -poll
* U.S. says Moscow behind separatists in eastern Ukraine
* Libya's preparations to load crude cap gains
* Coming up: API data Tuesday at 4:30 p.m. EDT (2030 GMT)
(Recasts and updates with settlement prices, adds analyst commentary)
NEW YORK, April 8 (Reuters) - U.S. crude oil prices rose more than 2 percent on Tuesday in a gradual, session-long rally driven by technical trading and bullish fundamentals such as a weaker U.S. dollar and forecasts for a draw on stockpiles of domestic oil products.
Fresh unrest in eastern Ukraine provided background support for Brent as traders worried that heightened tensions between Moscow and the Western powers might interrupt oil supply from Russia, one of the world's top oil exporters.
The U.S. Energy Information Administration said on Tuesday it did not assume that a disruption of oil supply or demand would result from the events in Ukraine.
The U.S. dollar fell near to three-week lows against a basket of six major currencies on Tuesday, which boosted buying of dollar-priced commodities such as oil.
Official government inventory data to be released Wednesday is expected to show U.S. oil stocks rose by 1.3 million barrels on average last week, according to a Reuters poll. However, analysts expect the data will also show gasoline stocks and stockpiles at the Cushing, Oklahoma, delivery point fell, which would be bullish for prices.
Technical trading boosted Brent and U.S. crude prices in addition to the support from fundamentals after both contracts fell to key lows on Monday, and bounced back in Tuesday's session.
"The seeds to today's prices were sowed yesterday," said Walter Zimmermann, chief technical analyst at United-ICAP in New Jersey.
"Both U.S. crude and Brent held exactly, to the penny, to a bull mark correction (level). The reaction to falling to that key level was (they) ricocheted higher."
U.S. crude rose $2.27 to hit a session high of $102.71 a barrel, before giving up some gains to settle $2.12 higher at $102.56 a barrel.
Brent rose $2.03 to a session high of $107.85 a barrel. It settled $1.85 higher at $107.67 a barrel.
Brent's premium over U.S. crude narrowed 27 cents to $5.11.
Limiting Brent's gains was the prospect that Libyan oil exports would rebound. Crude prices fell on Monday after news that rebels had agreed to gradually end their eight-month blockade of Libyan oil ports, which account for around 700,000 barrels per day.
However, Libya's National Oil Corp had not yet lifted a force majeure at the eastern ports on Tuesday.
The Ukraine government said the government-building occupation by pro-Moscow protesters that began Sunday is part of a Russian-led plan to dismember the country. U.S. Secretary of State John Kerry said he feared Moscow might repeat its Crimean operation.
NATO Secretary-General Anders Fogh Rasmussen warned Moscow that if it encroaches into eastern Ukraine, there would be "grave consequences" for its relationship with the alliance.
Analysts expect data to show U.S. oil stocks rose by 1.3 million barrels on average last week, while gasoline stocks fell by 700,000 barrels, a preliminary Reuters poll showed.
The American Petroleum Institute industry group will release its report Tuesday at 4:30 p.m. EDT (2030 GMT).
Official data from the U.S. Energy Information Administration is planned for release Wednesday at 10:30 a.m. EDT (1430 GMT).
News of an easing of tensions between the West and Iran kept a lid on global oil prices. Tehran said Monday it hoped for enough progress this week to enable negotiators to start drafting a final accord by mid-May to settle a long-running dispute over its nuclear program.
The Islamic republic and six world powers will hold a new round of talks in Vienna on Tuesday and Wednesday.
(Additional reporting by Ron Buosso in London; Editing by Jane Baird, Lisa Von Ahn, Bernadette Baum and Peter Galloway)