US WTI crude futures were at $ 64.57 a barrel at 0242 GMT, up 19 cents, or 0.2 per cent, from their previous settlement.
Brent crude futures were at $ 69.72 per barrel, up 19 cents, or 0.3 per cent.
The Middle East-dominated Organization of the Petroleum Exporting Countries (OPEC) together with a group of non-OPEC producers led by Russia in 2017 started cutting output in order to rein in oversupply and prop up the market.
Brent, off which OPEC prices most its crude exports, has risen by around a quarter since then, which has lead to speculation that the restraints on production may be lifted.
But sources at OPEC told Reuters this week that the group and its allies were set to keep their deal on cutting production for the rest of 2018.
“OPEC is in no rush to re-evaluate whether or not it should change the current production caps at the June meeting and may wait till later this year,” said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
Despite this, Brent remained below $ 70 and WTI under $ 65 per barrel, weighed by rising crude inventories and production in the United States.
Commercial US crude inventories rose by 1.6 million barrels in the last week <C-STK-T-EIA> to 429.95 million barrels, the Energy Information Administration (EIA) said on Wednesday.
US crude oil production hit a fresh record, at 10.43 million barrels per day (bpd) <C-OUT-T-EIA>. That puts the United States ahead in output of top exporter Saudi Arabia. Only Russia pumps out more, at 11 million bpd.
In China, Shanghai crude oil futures opened Thursday’s morning session down nearly 2 per cent, pushing the new market to parity with US prices.
That implies a disconnect between financial and physical crude markets, as US crude has been exported to China profitably for the last two years.
The latest drop takes the fall since the contract’s launch on Monday to 10 per cent.