* U.S. dollar falls after rise in jobless claims
* Iran's nuclear stance, Nigeria violence in focus
(Recasts, updates prices)
By Jane Merriman
LONDON, July 31 (Reuters) - Oil was near $126 a barrel on Thursday, supported by a weaker U.S. dollar, but pressured by bearish data on the economy in top energy consumer the United States.
U.S. light crude for September <CLc1> was down 37 cents at $126.40 a barrel by 1336 GMT, after a jump of $4.58 on Wednesday.
London Brent crude <LCOc1> was 95 cents down at $126.15 a barrel.
An unexpected jump in U.S. weekly jobless claims put pressure on the U.S. dollar, which briefly caused oil to make further gains on Thursday, but these proved short-lived.
Oil has tended to rise when the dollar falls and vice versa, but this pattern has shown signs of breaking down recently.
U.S. gross domestic product grew at a 1.9 percent annual rate in the second quarter, lower than expected [
].Oil had rallied strongly on Wednesday after a surprise fall in gasoline stocks last week in the United States. [
]This followed a fall of about 18 percent from the market's record peak above $147 on July 11, partly due to concerns over demand erosion, especially in the United States.
This was the biggest drop on record in dollar terms.
"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."
RECORD RUN
Oil's six-year advance has been driven partly by strong demand growth from emerging economies such as China, India and the Middle East that could tighten the market's supply/demand balance over the long term.
Investors have piled into oil and other commodities as a hedge against inflation and as a more attractive play than bearish equity markets.
The weak U.S. dollar has also contributed to oil's record run as it is priced in the U.S. currency.
Analysts are not yet convinced that the sharp fall this month means the bull market in oil is over.
"Although oil prices have fallen around $20 from their peak, support at $120 held and that means there is the potential for prices to rise back to record levels again," said Shuji Sugata, manager at Mitsubishi Corp Futures and Securities Ltd in Tokyo.
Analysts who track the market's movements on charts are waiting to see if the price can continue to hold above the $120 a barrel level.
Political tensions that have helped underpin the market returned to the spotlight when Iran said it would press ahead with its nuclear development plans.
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.
Rival militant factions in Nigeria's oil-producing Niger Delta have clashed this week in an apparent turf war, killing at least four people.
The fighting illustrates the deteriorating security situation in the Delta, the hub of Nigeria's oil industry, where unrest has shut down around a fifth of output. (Additional reporting by James Topham in Tokyo; editing by Anthony Barker)