* Oil falls more than 2 percent on weak U.S. jobs claims
* Demand concerns weigh
* Iran's nuclear stance, Nigeria violence in focus
(Recasts, updates prices, market activity; new byline, dateline, previously LONDON)
By Matthew Robinson
NEW YORK, July 31 (Reuters) - Oil fell more than 2 percent on Thursday as weak U.S. economic data reinforced worries about shrinking fuel demand in the world's top energy consumer.
U.S. crude <CLc1> traded down $2.70 at $124.07 a barrel by 1:15 p.m. EDT (1715 GMT), partially erasing a jump of $4.58 on Wednesday. London Brent crude <LCOc1> gave up $2.77 to trade at $123.33 a barrel.
A report from the U.S. Labor Department showing an increase in U.S. jobless claims added to worries high energy prices and a soft economy are eroding fuel demand.
U.S. gasoline consumption has trailed last year's levels by about 1.5 percent as pump prices hit record highs this summer, according to the most recent government data. Demand growth also has been hit in Europe.
"Declining levels of demand are still in the forefront of the market," said Gene McGillian, analyst at Tradition Energy.
Tempering some of the gains, rebel attacks in Nigeria this week shut 40,000 bpd of output from Royal Dutch Shell <RDSa.L>, adding to a string of bombings that has disrupted the OPEC nation's production.
Dealers also have been on edge due to the threat of hurricanes denting production in the Gulf of Mexico.
"Supply snags, like Shell saying only 40,000 barrels per day (bpd) were shut by the pipeline attack in Nigeria, have so far been minimal and nothing is going on in the tropics," McGillian said.
Oil hit a record over $147 on July 11, the peak of a six-year rally set in motion by strong demand from Asian economies like China. Additional support this year has come from investors seeking to hedge against inflation and the weak dollar by buying into commodities markets.
Traders have also been watching political tensions between the West and OPEC member Iran over Tehran's nuclear program, which some dealers say pose a threat to Middle East exports.
Western powers had given Iran two weeks from July 19 to respond to their offer to hold off imposing more U.N. sanctions if Tehran would freeze any expansion of its nuclear work.
Oil rallied on Wednesday after a government report showed a surprise fall in U.S. gasoline stocks last week. [
]"There was a gasoline-led rally, but now I think it's running out of puff. It seems to need constant bullish news at the moment to push it up," said Christopher Bellew, of Bache Commodities. "Everyone is talking about demand destruction." (Additional reporting by Robert Gibbons in New York, Jane Merriman in London and James Topham in Tokyo; Editing by David Gregorio)