Prices were supported by widely-watched data showing a larger-than-expected drawdown in US crude oil inventories, with government data due later in the day.
Brent crude futures for September delivery were trading up $0.64 at $63.04 a barrel by 1136 GMT.
US crude futures for August were up $0.47 at $56.72 a barrel. Both benchmarks fell more than 4% on Tuesday over worries about a slowing global economy.
The Organisation of the Petroleum Exporting Countries (OPEC) and other producers such as Russia, a group known as OPEC+, agreed on Tuesday to extend oil supply cuts until March 2020 as members overcame differences to try to prop up prices.
"We had a pretty sharp correction yesterday (Tuesday) so after that, a little rebound is expected. Globally, the market is concerned about oil demand growth potential," Olivier Jakob of Petromatrix consultancy said.
"Extending the cut by six or nine months, it doesn't really matter if the level stays the same. If you (OPEC) really wanted to target stock levels, you would need deeper cuts but Saudi Arabia has already gone beyond its cut target."
Ahead of government data due later on Wednesday, industry group the American Petroleum Institute (API) said that US crude inventories fell by 5 million barrels last week, more than the expected decrease of 3 million barrels.
The OPEC+ agreement to extend oil output cuts for nine months should draw down oil inventories in the second half of this year, boosting oil prices, analysts from Citi Research said in a note.
"Keeping cuts through the end of 1Q aims to avoid putting oil into the market during a seasonal low for demand and refinery runs," they said.
Still, signs of a global economic slowdown hitting oil demand growth worried investors after global manufacturing indicators disappointed and the United States opened another trade front after threatening the EU with more tariffs.
Barclays expects demand to grow at its slowest pace since 2011, gaining less than 1 million barrels per day year-on-year this year.
Morgan Stanley, meanwhile, lowered its long-term Brent price forecast on Tuesday to $60 per barrel from $65 per barrel, and said the oil market is broadly balanced in 2019.
Crude prices were also capped by signs of a recovery in oil exports from Venezuela in June and growth in oil production in Argentina in May.
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