* Libya hopes to restart El Sharara output pressures crude prices
* Brent crude oil set for biggest weekly fall in six months
* U.S. crude loses over $1 earlier in session
* U.S. weekly crude stocks down 7 million barrels vs forecast of 3 million -EIA
(Updates prices, changes byline, dateline (previous LONDON)
NEW YORK, Jan 3 (Reuters) - Crude oil prices dropped on both sides of the Atlantic for the fourth straight session on Friday as traders anticipated the return of Libyan oil and U.S. inventory data hinted at weak demand.
Libya hopes to resume production at one of its largest oilfields, El Sharara in the west of the country, within three days after protesters agreed to suspend their two-month stoppage, officials said on Thursday.
An increase in oil exports from the OPEC member, which have dropped to less than 250,000 barrels per day (bpd) from 1.4 million bpd in July, would boost supply and weigh on prices.
Crude oil inventories in the United States fell for the fifth straight week, shedding seven million barrels in the week ended Dec. 27, weekly U.S. Energy Information Administration data showed on Friday. This was more than double analysts' expectations for a three million barrel drop.
Analysts attributed the drop to a tax incentive that encourages oil companies to draw down inventory at year-end, noting that a five million barrel build in distillate stocks implied demand was weak.
"This is the continued drawing-down for year-end book-keeping purposes. I think going forward, all this oil starts showing up again," said Gene McGillian, analyst at Tradition Energy in Stamford, Connecticut.
Brent fell 72 cents to $107.06 by 12:33 p.m. EST (1733 GMT). The losses followed Thursday's 2.7 percent fall and set the European benchmark on track for its biggest weekly percentage drop in six months.
U.S. crude fell 93 cents to $94.51 and was on track for a weekly percentage fall of more than 5 percent, its sharpest since September 2012.
The prospect of an increase in Libyan oil exports is more likely than previous false starts because it was coming from the west of the country, said oil analyst Olivier Jakob of Petromatrix in Zug, Switzerland.
"What has really failed to materialize so far has been a restart in the east, where you have autonomy groups that are controlling the ports," he said.
"In the west, it's a different situation because it was a protest at the field, but the port is actually open. If they restart production it can really move to the market."
(Additional reporting by Joshua Franklin in London, Florence Tan in Singapore; Editing by William Hardy and Diane Craft)