U.S. crude for February delivery was 13 cents higher at $36.10 a barrel at 0419 GMT (11.19 p.m. ET Tuesday), after slipping 79 cents in the previous session.
Brent crude prices were up 12 cents at $36.54 a barrel, after closing down 80 cents. Brent hit an 11-year low of $35.98 a barrel just before Christmas.
"Crude oil oversupply is still in play; however the deficit between demand and supply is getting smaller," said Daniel Ang, an investment analyst at Phillip Futures, in a note on Wednesday. "Possible changes to global supply should come from the U.S. and Iran."
Iranian oil exports are widely expected to increase in 2016 as Western sanctions against the country for its alleged nuclear weapons program are likely to be lifted.
Still, a senior Iranian oil official said the country could moderate oil output and exports once the sanctions are lifted to avoid putting prices under further pressure.
"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."
Concerns over mounting stock levels continue to add pressure to prices, with crude inventories in the United States likely to have risen by 439,000 barrels last week, according to a Reuters poll of eight analysts.
The U.S. Energy Information Administration (EIA) will publish its closely watched weekly data at 1530 GMT (10.30 a.m. ET).
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.
"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 which hovered near a one-month high reached on Tuesday as traders sought safer havens.
