Despite this, the outlook for next year remains muted on the back of an economic slowdown.
International Brent crude oil futures were at $62.02 per barrel at 0601 GMT, up 35 cents, or 0.6 percent, from their last close.
Prices surged on Friday after the Organization of the Petroleum Exporting Countries (OPEC) and some non-OPEC producers including heavyweight Russia announced they would cut oil supply by 1.2 million barrels per day (bpd), with an 800,000-bpd reduction planned by OPEC members and 400,000 bpd by countries not affiliated with the group.
The shutdown of the 315,000-bpd El Sharara oilfield in Libya also helped push Brent, traders said.
U.S. West Texas Intermediate (WTI) crude futures were weaker, however, dropping 12 cents from their last settlement to $52.59 per barrel, weighed by surging U.S. output as the booming American oil industry is not taking part in the announced cuts.
The OPEC-led supply curbs will be made from January, measured against October 2018 output levels.
"Our key conclusion is that oil prices will be well supported around the $70 per barrel level for 2019," analysts at Bernstein Energy said on Monday.
Despite the cuts, that was still a price forecast reduction of $6 per barrel as Bernstein lowered its crude oil demand forecast from 1.5 million bpd previously to 1.3 million bpd for 2019.
U.S. bank Morgan Stanley said the cut was "likely sufficient to balance the market in 1H19 and prevent inventories from building".
It added that it expected "Brent to reach $67.5 per barrel by 2Q19, down from $77.5 before."
Not all analysts expect the cuts to be sufficient to end oversupply.
Edward Bell, commodity analyst at Emirates NBD bank, said in a note on Sunday that "the scale of the cuts...isn't enough to push the market back into deficit" and that he expected "a market surplus of around 1.2 million bpd in Q1 with the new production levels."
Oil prices have fallen sharply since October on signs of an economic slowdown, with Brent losing almost 30 percent in value.
Japan, the world's third-biggest economy and No.4 oil consumer, on Monday revised its third quarter GDP growth down to an annualised rate of minus 2.5 percent, down from the initial estimate of minus 1.2 percent.
Meanwhile the two world's biggest economies, the United States and China, are locked in a trade war which is threatening to slow global growth and battering investor sentiment.
Despite the expectations of a slowdown, physical demand on the ground remains healthy.
China, the world's biggest oil importer, over the weekend reported November crude oil imports rose 8.5 percent from a year ago, to 10.43 million bpd, marking the first time China imported more than 10 million bpd. That leaves the world's second-biggest economy on track to set yet another annual import record.
Strong demand is being driven by Chinese purchases for strategic reserves, but also by new refineries, triggering excess supply of fuels, filling up storage tanks and eroding refinery profits across Asia.