* Saudi-Iran split dashes chance of OPEC deal to curb oil glut
* Iran may moderate output once sanctions are lifted - official
* U.S. crude stocks fell 5.6 million barrels last week -API
* Coming up: EIA to publish inventory data at 1530 GMT
By Jacob Gronholt-Pedersen
SINGAPORE, Jan 6 (Reuters) - Oil prices edged higher on Wednesday, rebounding from near 11-year lows in the previous session as concerns over growing supply and rising stock levels outweighed tensions between key Middle East producers.
A rift between Saudi Arabia and Iran over the Saudi execution of a Shi'ite cleric failed to boost prices this week, as it appeared to put an end to speculation that OPEC members could agree production cuts to lift prices. urn:newsml:reuters.com:*:nL8N14P2QH
U.S. crude for February delivery CLc1 was 19 cents higher at $36.16 a barrel at 0124 GMT, after slipping 79 cents in the previous session.
Brent crude prices LCOc1 were up 18 cents at $36.60 a barrel, after closing down 80 cents.
"Geopolitical tension presents the greatest upside risk to the crude market, at least through the first half of the year," said Matt Smith, an analyst for energy database Clipper Data.
Still, a senior Iranian oil official said the country could moderate oil output and exports once Western sanctions are lifted to avoid putting prices under further pressure. urn:newsml:reuters.com:*:nL8N14P2Z1
"We don't want to start a sort of a price war," Mohsen Qamsari, director general for international affairs of the National Iranian Oil Company (NIOC), told Reuters in an interview.
"We will be more subtle in our approach and may gradually increase output," Qamsari said. "I have to say that there is no room to push prices down any further, given the level where they are."
However, concerns over mounting stock levels added pressure to prices, with crude inventories in the United States rising by 439,000 barrels last week, according to a Reuters poll of eight analysts. urn:newsml:reuters.com:*:nL1N14P1FU
The U.S. Energy Information Administration (EIA) will publish its closely watched weekly data at 1530 GMT.
Data from American Petroleum Institute (API), an industry group, showed crude stocks fell last week by 5.6 million barrels, while stocks at the Cushing, Oklahoma, delivery hub rose by 1.4 million barrels. API/S
"Demand growth and slowly declining non-OPEC crude production will stabilize (crude stock levels) in 2016 but not substantively reduce them until 2017," analysts at PIRA Energy said in a note.
The oil market also faced pressure from a strengthening dollar .DXY which hovered near a one-month high reached on Tuesday as traders sought safer havens. USD/