US WTI crude futures were at $ 63.2 a barrel at 0117 GMT, up 18 cents, or 0.3 per cent, from their previous settlement.
Brent crude futures rose to $ 67.84 per barrel, up 20 cents, or 0.3 per cent, after it fell more than 2 per cent on Monday.
Greg McKenna, chief market strategist at futures brokerage AxiTrader, said traders were wary of the fact that the market was still holding large amounts of long positions which will need to be sold off at some stage.
“That makes prices vulnerable to bad news,” he said, pointing to rising Russian production and a likely drop in Saudi physical crude prices.
Brent reached a 2018 high of $ 71.28 in January but has since struggled to pass that level. Two rallies last week ran out of steam just above $ 71.
There was also pressure coming from the physical market, where top exporter Saudi Arabia is expected to cut prices for all crude grades it sells to Asia in May.
This came amid rising supplies. Top producer Russia pumped 10.97 million barrels per day (bpd) of crude in March, up from 10.95 million bpd in February, official data showed, an 11 month high.
One of the key price drivers going forward will be crude output from the United States <C-OUT-T-EIA>, which has risen by almost a quarter since mid-2016 to 10.43 million bpd, overtaking Saudi Arabia’s and coming in just shy of Russia’s.
A dip in drilling activity for new production could imply that the relentless rise in US production could be tapering off towards the middle of the year.
“Production data released on Wednesday (in the United States) will offer a fresher clue on which direction prices are going,” Ma Kun, general manager of Energy and Chemicals at Bank of China International Futures said.
Weekly official Energy Information Administration (EIA) data, which includes production figures, is due to be published on Wednesday.