* Iran says wants to resolve nuclear row within months
* EIA data shows 2.6 mln barrel gain in US crude stocks
NEW YORK, Sept 26 (Reuters) - Oil prices firmed on Thursday in light trading, despite easing political worries and an improving supply picture, as traders sought bargains after sharp losses earlier this month.
Despite a strong run toward the end of the session, both Brent and U.S. crudes are still down over 4 percent in September. Both have shed nearly $8 from peaks earlier in the month as fears have faded about conflict in the Middle East.
Those steep declines brought some buyers back into the market on Thursday, analysts said, particularly as the trading session for U.S. crude came to a close.
"The market stalled out to the high side, and when it's not really following through, you're getting short-covering into the close," said Bill Baruch, senior market strategist at iitrader.com in Chicago.
"We've been seeing this quite often."
Brent oil gained 89 cents to $109.21 a barrel.
U.S. crude futures rose 37 cents to $103.03 a barrel, its first day of gains following five straight sessions of losses.
"It's a nice technical bounce. For five straight days we had a lot of value erosion, and it's completely understandable we would have some consolidation and a little bit of a rebound," said Addison Armstrong, senior director of market research at Tradition Energy in Stamford, Connecticut.
Total U.S. and Brent crude trading volumes were 37 percent below their respective 30-day averages. Volume for RBOB gasoline futures also was 37 percent under its 30-day average, with heating oil futures volume trailing its 30-day average by 23 percent.
"The thin market is what we were hearing on the volatility near the end of the (open outcry) session," said a New York-based broker.
Brent's late run pushed the spread between the two benchmarks to $6.18, up from Wednesday's close of $5.66.
U.S. Secretary of State John Kerry said he looked forward to a "good meeting" with Iran and major powers on Thursday, and a U.S. official said China agreed that Iran should respond positively to existing proposals on Iran's nuclear program.
Iran's new government said on Wednesday it wanted to "jump-start" talks with world powers to resolve a decade-long dispute over its nuclear program and hoped for a deal in three to six months.
This pushed oil down in late trading in New York on Wednesday after earlier strength.
Iranian Foreign Minister Mohammad Javad Zarif is set to hold talks on the nuclear issue on Thursday afternoon in New York with Kerry as well as diplomats from Britain, France, Russia, China and Germany.
The West's standoff with Iran over the OPEC member's nuclear program has helped support oil prices for nearly a decade. Years of sanctions have cut Iranian oil exports by more than 1 million barrels per day.
At the same time, Iran has sharply criticized the International Atomic Energy Agency, the U.N. nuclear watchdog, over "baseless allegations" about its atomic activity, a document showed. The posting of the document on the IAEA's website comes before talks between the two sides on Friday to discuss a stalled inquiry into suspected bomb research by Tehran.
An impasse over the U.S. government budget and weak lending data in the euro zone kept enthusiasm in check for risk-sensitive assets such as oil.
The demand/supply balance was also capping prices, analysts said.
"With weaker fundamentals still ahead, oil prices (are) likely to remain under pressure," Morgan Stanley analysts said in a note on Thursday.
Supply was recovering from Libya, and bigger U.S. stockpiles were putting pressure on prices.
Oil inventories in the United States rose 2.6 million barrels to 358 million barrels last week, data from U.S. Energy Information Administration showed.
The data also showed U.S. exports of refined products last week reached the highest level on record at 3.4 million barrels per day, 17.5 percent higher than a year ago, as refineries processed crude at high rates.