* Libya says will sue firms who buy oil from protesters
* EIA reports build at Cushing, strong rise in gasoline
* U.S. oil supported by frigid weather
(Adds analyst's quote, updates prices; changes byline and dateline, previous LONDON)
NEW YORK, Jan 8 (Reuters) - Brent crude oil rose on Wednesday on continued concerns over Libyan oil supply, while U.S. crude oil fell after government data showed a build in stockpiles at the U.S. benchmark delivery point.
Libyan unrest boosted Brent's geopolitical premium, sending U.S. oil's discount to the European benchmark to a one-month low of more than $14 a barrel.
Libya's civil unrest over the last seven months has interrupted oil exports. On Wednesday the Libyan oil minister said the country would sue and stop doing business with any foreign firms that buy oil from ports seized by protesters, after those protesters offered oil at $90 a barrel.
Libyan Prime Minister Ali Zeidan warned its navy could sink oil tankers that approach eastern ports controlled by armed protesters led by tribal leader and 2011 civil war hero Ibrahim Jathran.
In the U.S., crude stockpiles at the U.S. oil futures contract delivery point in Cushing, Oklahoma, rose by more than a million barrels, data from the U.S. Energy Information Administration (EIA) showed. As well, gasoline and distillate stocks, including diesel and heating oil, each rose much more than expected, indicating slack demand.
"When you put in 12 million barrels of fuel stocks ... that doesn't paint a strong fundamental picture," said Gene McGillian, energy analyst with Tradition Energy in Stamford, Connecticut.
U.S. gasoline futures prices fell to a session low of $2.6533 a gallon after the data and were last trading less than a penny lower at $2.6708.
Brent crude was up 30 cents at $107.65 a barrel at 12:10 p.m. EST (1710 GMT). The contract edged above its 200-day moving average at $107.44, a key technical indicator watched by traders.
U.S crude was down 50 cents at $93.17 a barrel.
Brent's premium over U.S. crude widened to $14.53 and earlier in the session touched a month high of $14.67.
Brent has been underpinned by tensions in Libya that have cut exports to around 510,000 barrels per day (bpd) from more than 1 million bpd in July, when the strikes began.
The government is expected to increase some exports, however, following the restart of the 350,000 bpd El Sharara oilfield at the weekend. The first exports of crude from El Sharara since October are expected to load around Jan. 10-12 from the government-controlled port of Zawiya, traders said.
In the meantime, losses in U.S. crude were capped by freezing weather in North America, which boosted demand for heating oil and has led to temporary malfunctions and closures at at least five refineries in the United States and Canada.
(Additional reporting by David Sheppard in London, Anna Louie Sussman in New York and Jacob Gronholt-Pedersen in Singapore; Editing by William Hardy and Chris Reese)