Despite this, crude prices remain well below recent highs due to signs of lingering oversupply, including rising US inventories and ample physical flows globally.
US West Texas Intermediate (WTI) crude futures were at $59.17 a barrel at 0123 GMT (6:53 am in India), down 2 cents from their last settlement. WTI was trading above $65 in early February.
Brent crude futures were at $62.77 per barrel, up 5 cents from their last close. Brent was above $70 a barrel earlier this month.
Ongoing weakness in the US dollar, which potentially stokes demand from countries using other currencies at home, as well as healthy economic growth were supporting oil markets, traders said.
"While we continue to see a firming fundamental backdrop over the course of this year ... investors should not discount the caution signs that have been emerging," investment bank RBC Capital Markets said in a note to clients.
"Pockets of oversupply have been emerging in the physical market," the Canadian bank said, adding that "the tempering physical oil backdrop is ... playing a central role in the recent price softness".
The American Petroleum Institute said on Tuesday that US crude inventories rose by 3.9 million barrels in the week to February 9, to 422.4 million.
That was largely due to soaring US crude production, which has jumped by over 20 per cent since mid-2016 to over 10 million barrels per day (bpd), surpassing output of top exporter Saudi Arabia and coming within reach of Russia, the world's biggest producer.
US crude is increasingly appearing on global markets.
More is set to come as the Louisiana Offshore Oil Port in the Gulf of Mexico starts testing supertankers for exports.
The surge in US production and exports means oil may be in oversupply again soon, flipping a deficit from 2017 induced by supply restraint led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia.
The International Energy Agency said on Tuesday oil demand would grow by 1.4 million bpd in 2018, but added output growth could outpace demand.
The physical market is already reacting, with prices for regional crude from the North Sea, Russia, the United States, and Middle East becoming cheaper as producers struggle to remain competitive amid ample supplies.
Despite the warning lights from within oil markets, economic fundamentals remain healthy.
High consumer spending drove Japan's economy to eight straight quarters of growth in October-December, its longest continuous expansion since the 1980s bubble economy, Cabinet Office data showed on Wednesday.