Brent crude futures rose 28 cents, or 0.4%, to $63.46 a barrel by 0650 GMT, after dropping 1% overnight - the first fall in four sessions.
U.S. West Texas Intermediate crude was up 27 cents, or 0.5%, at $56.15 a barrel, having dropped 1.6% in the previous session.
"We see it as a current tug of war between the bull case of OPEC production cuts, political risk in the Gulf and the recent reduction in crude inventories, versus the bear case of slowing global growth and a ramp-up in U.S. production," said Hue Frame, managing director at Frame Funds in Sydney.
The overall sentiment in the oil market has darkened as investors worry that slowing global economic growth will weaken demand for oil.
Adding to a recent string of downward revisions for the oil market, Energy consultancy FGE lowered its 2019 global oil demand growth to average 740,000 bpd in 2019.
A series of purchasing manager index readings in the United States and Europe were weaker than expected, confirming concerns about slower economic growth amid a trade war between the United States and China.
"It's not economic uncertainty we should be worried about rather its the doom and gloom economic realities that the key forward-looking manufacturing PMI's are telling us about the dismal health of this rapidly deteriorating global macro environment," said Stephen Innes, managing partner at Vanguard Markets.
Set against those worries are ongoing tensions in the Middle East following the seizure of a British-flagged tanker in the Gulf by Iranian forces last week.
The military adviser to Iran's supreme leader was quoted on Wednesday as saying that any change in the status of the Strait of Hormuz, which Tehran says it protects, would open the door to a dangerous confrontation.
Britain, meanwhile, gained initial support from France, Italy and Denmark for its plan for a European-led naval mission to ensure safe shipping in the Gulf.
Meanwhile, U.S. crude stocks fell by nearly 11 million barrels last week, well above analysts' expectations for a drop of 4 million barrels.