International Brent crude oil futures were at $76.51 per barrel at 0037 GMT, up 30 cents, or 0.4 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude futures were up 24 cents, or 0.4 percent, at $69.11 a barrel.
Despite some concerns about an economic slowdown because of trade conflict between the United States and China, crude supplies are relatively tight due to disruptions as well as voluntary restraints on output by the Organization of the Petroleum Exporting Countries (OPEC).
The cartel's monitoring committee found that oil producers participating in a supply-reduction agreement, which includes non-OPEC member Russia, cut output in July by 9 percent more than called for.
The findings for last month compare with a compliance level of 120 percent for June and 147 percent for May, meaning participants have been steadily increasing production.
OPEC and its allies agreed in late 2016 to cut output from 2017 by around 1.8 million barrels per day (bpd) versus October 2016 levels.
The International Energy Agency (IEA) on Monday warned of further supply disruptions, especially from Venezuela, where an economic crisis has cut deep into the OPEC-member's oil output.
Venezuelan crude oil exports had halved in the previous two years to just 1 million bpd by mid-2018, according to trade flow data.
"We can expect a further fall," the IEA's Executive Director Fatih Birol told Reuters in Norway on Monday.
Birol also warned that African OPEC-members Libya and Nigeria "seem both still fragile countries" despite some recent improvements.
Birol said it was too early to gauge the impact of the U.S. sanctions that will target Iran from November.