There is still some scepticism in the market over whether OPEC will cut output further, however, with many analysts expecting only an extension of existing cuts
Oil prices rose on Wednesday ahead of a meeting of OPEC and its allies to discuss whether to extend production curbs to support the market, while industry data showing that US crude stockpiles fell more than expected helped to lift prices.
Brent crude LCOc1 futures were up 35 cents, or 0.6%, at $61.17 a barrel by 0246 GMT.
US West Texas Intermediate (WTI) crude CLc1 futures were up by 31 cents, or 0.6%, at $56.41.
The Organization of the Petroleum Exporting Countries (OPEC) and allies that include Russia - a group known as OPEC+ - are preparing to approve deeper crude output cuts this week, when they meet in Vienna, according to Iraq, the group's second-biggest producer.
Thamer Ghadhban, the oil minister of Iraq, told reporters on Tuesday in Vienna that "a deeper cut is being preferred by a number of key members".
There is still some scepticism in the market over whether OPEC will cut output further, however, with many analysts expecting only an extension of existing cuts.
"We ... think OPEC could announce an extension to supply cuts to cover the whole of 2020 rather than the three to six months the market is currently factoring in," BNP Paribas Markets said in a note.
An extension "with an option to review policy at the next meeting, would send a strong message of commitment by signatories of the Declaration of Cooperation," the BNP Paribas analysts said.
OPEC members meet on Thursday and then on Friday the OPEC+ group meets. OPEC+ has been curbing supply since 2017 and is expected to keep the cuts in place to balance out record production in the United States.
Crude oil inventories in the US fell by more than expected last week, according to the industry group American Petroleum Institute. Stockpiles of crude oil fell by 3.7 million barrels, more than double expectations of a decline of 1.7 million barrels.
Gasoline and distillate stocks increased, however, and the market will be looking for confirmation of the crude draw when official figures come out from the US Department of Energy's Energy Information Administration later on Wednesday.
Keeping a lid on prices are the dwindling prospects of a trade deal between the United States and China. The trade dispute between the world's two biggest economies has weakened the global economy and held back oil demand growth.
US President Donald Trump said on Tuesday an agreement to end the trade dispute may have to be delayed until after the American presidential election in November 2020.
"Both contracts should remain supported at these levels despite the (US-China) trade concerns as the market looks to the start of the OPEC+ meeting tomorrow," said Jeffrey Halley, senior market analyst at OANDA.