* U.S. gasoline stocks fall 5.2 mln barrels, over 7 times forecast -EIA
* Weaker U.S. dollar boosts oil buying
* Russia seeks to reassure West, Ukraine over troops
* Libya not in full control of re-opened eastern port
(Rewrites top, updates prices)
NEW YORK, April 9 (Reuters) - U.S. crude rose by $1 on Wednesday as a rally that started with high gasoline demand was boosted by technical trading, while Brent crude rose modestly due to the tense relations between Russia and the West.
U.S. crude oil stocks rose more than expected last week, but the build was overshadowed by a sharp spike in gasoline demand, according to U.S. Energy Information Administration data.
The data drove U.S. gasoline and crude oil prices above a key technical level and drove the closely watched and traded price spread with Brent, the European benchmark, to the narrowest point since mid-September.
Investors continued to worry that Moscow's standoff with the West could quickly take a turn for the worse, underpinning prices for Brent.
Assistant U.S. Secretary of State Victoria Nuland said on Wednesday that Washington has no doubt that Russians were behind the takeovers of government buildings in eastern Ukraine this week.
Meanwhile, Moscow called concerns from the West over the presence of Russian troops near the border of Ukraine "groundless", saying they posed no threat.
"Gasoline is going to push the market higher and bring U.S. crude up with it," said Joseph Posillico, senior vice president of energy derivatives at Jefferies Bache in New York.
U.S. RBOB gasoline rose by 1.5 cents after the EIA data was released, and was last trading 2-1/2 cents higher at $3.0049 per gallon at 2:02 p.m. EDT (1802 GMT).
U.S. oil rose as much as $1.03 to a session high of $103.59 a barrel, and was last trading 85 cents higher at $103.41 a barrel.
Brent crude rose 28 cents to $107.96 a barrel.
Brent prices were not bothered by the potential for a rebound in Libyan oil exports as the country's oil protection force said it has not regained full control of the Zueitina port. The government had announced a deal with rebels to end the blockade of eastern oil terminals earlier this week.
The port, along with the country's two largest, Es Sider and Ras Lanuf, has been under the control of an eastern federalist group led by former guard member Ibrahim al-Jathran, who recruited men from within his ranks.
U.S. crude inventories rose by 4 million barrels in the week to April 4, data from the Energy Information Administration (EIA) showed, compared with analysts' expectations for an increase of 1.3 million barrels.
But analysts were focused on the steeper-than-expected fall in gasoline stocks, which they said added to evidence of a broad economic recovery and robust demand as summer driving season gets started.
Gasoline stocks fell by 5.2 million barrels, dwarfing the 729,000-barrel-draw that was expected.
"The gasoline demand is jaw dropping. Here we are in the first week of April and gasoline demand is pretty strong," said Carl Larry of consultancy Oil Outlooks.
"The more jobs we've seen created, the more people back to work has really driven gasoline demand back up."
(Additional reporting by Peg Mackey in London and Manash Goswami in Singapore; Editing by Jane Baird, David Evans, Tom Brown and Nick Zieminski)