Prices rose early, then pared most gains after data showed US crude inventories fell by 1.1 million barrels in the latest week, a much smaller decline than the 3 million barrel decrease analysts had expected.
"The market is disappointed by a very small crude oil inventory draw ... the only sign of strength in the market is the continued modest decline of gasoline inventories" said Andrew Lipow, president at Lipow Oil Associates in Houston.
US crude imports rebounded while exports fell sharply from a record 3.8 million barrels per day (bpd) a week earlier, analysts said.
September Brent crude futures were up 65 cents, or 1pc, at $63.05 a barrel by 11:57 a.m. ET (1557 GMT).
US crude futures for August delivery were up 24 cents, or 0.4pc at $56.49 a barrel. On Tuesday, both benchmarks fell more than 4pc on worries about a global economic slowdown.
US gasoline futures led the energy complex, rising about 1.5 percent to $1.8974 a gallon.
"We had a pretty sharp correction yesterday so after that, a little rebound is expected. Globally, the market is concerned about oil demand growth potential," Olivier Jakob of Petromatrix consultancy said.
Trading volumes were subdued ahead of the US Fourth of July holiday on Thursday. Some 450,892 lots of the front-month US crude futures contract were traded, about half of the previous session's volume.
On Tuesday, the Organization of the Petroleum Exporting Countries and other producers such as Russia, a group known as OPEC+, agreed to extend oil supply cuts until March 2020.
"Extending the cut by six or nine months, it doesn't really matter if the level stays the same," Jakob said.
"If you (OPEC) really wanted to target stock levels, you would need deeper cuts but Saudi Arabia has already gone beyond its cut target."
The OPEC+ agreement should draw down oil inventories in the second half, 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 worried investors after global manufacturing indicators disappointed and the United States threatened Europe with more tariffs.
The US trade deficit jumped to a five-month high in May and the ADP National Employment Report showed private payrolls increased far less than economists had expected.
Barclays expects oil demand to grow at its slowest pace since 2011.
Morgan Stanley lowered its long-term Brent price forecast to $60 per barrel from $65 per barrel, and said the oil market is broadly balanced.
Crude prices also were pressured by signs of a recovery in oil exports from Venezuela in June and growth in oil production in Argentina in May.