Brent crude futures were at $62.51 per barrel at 0807 GMT, 29 cents, or 0.5 percent above their last close.
US West Texas Intermediate crude was at $56.60 a barrel, up 18 cents, or 0.3 percent.
Traders said markets were generally supported by ongoing production cuts led by the Organization of the Petroleum Exporting Countries.
OPEC, together with a group of non-OPEC producers led by Russia, has been restraining output since the start of this year in a bid to end a global supply overhang and buoy prices.
The deal to curb output is due to expire in March 2018, but OPEC will meet on Nov. 30 to discuss the outlook for the policy.
OPEC is expected to agree to extend cuts as storage levels remain high despite recent drawdowns, although there are doubts about the willingness of some participants to continue to restrict their production.
“If the OPEC/non-OPEC cuts continue, the stocks surplus will reduce to just some 50 million barrels above the five-year average in Q3 2018 (down from 140 million barrels above that average now) and prices will hit $65-70 per barrel,” energy consultancy FGE said.
The biggest headache for OPEC has been rising US drilling activity, led by shale oil producers.
Energy consultancy Westwood Global Energy Group said US output would climb even faster than implied by the rising rig count, which has jumped from 316 rigs in mid-2016 to 738 last week, as producers get more productive per well.
“Westwood Global Energy forecasts an 18 percent increase in active rigs in 2018, but more rapid demand growth in certain service areas as operators focus on efficiency and delivering more for less,” the consultancy said.
For 2018, FGE warned potential supply disruptions during an already tighter market could trigger oil price spikes. But it said the market could slump again toward 2019 as US output continues to soar and OPEC and its allies at some point will stop withholding output.
“We see another big rush with (US) production growth of some 1-1.5 million bpd in 2018 and 2019,” FGE said. It added that OPEC also “has some 1.5 million bpd of spare capacity (while) Russia and Kazakhstan could also add another 500,000 bpd.”
Reflecting rising US oil exports to Asia, US commodity exchange CME Group said it will list a new futures contract that prices the spread between US WTI futures and Middle East benchmark Dubai, starting Dec. 18.