Saudi Energy Minister Khalid al-Falih said his country would limit crude oil exports at 6.6 million barrels per day in August, almost 1 million bpd below levels a year ago.
Russian Energy Minister Alexander Novak also told reporters that an additional 200,000 bpd could be removed from the market if compliance with a global deal to cut output was 100 percent.
Brent crude futures settled up 54 cents or 1.1 percent to $48.60 a barrel. US West Texas Intermediate (WTI) crude futures settled up 57 cents or about 1.3 percent to $46.34 a barrel.
The Saudi and Russian energy ministers were in St. Petersburg for a gathering of the Organization of the Petroleum Exporting Countries and other producers. Ministers discussed their previous agreement to cut production 1.8 million bpd from January 2017 through March 2018.
Falih said OPEC and non-OPEC partners were committed to cut output longer if necessary but would demand that non-compliant nations stick to the agreement.
OPEC members Nigeria and Libya have been exempt from the output cuts, and market watchers remain concerned that production from the two countries is offsetting the impact of the global reduction.
There was no discussion of deeper output cuts, and OPEC Secretary-General Mohammad Barkindo said Nigeria had no intention of going beyond its production target of 1.8 million bpd.
Libya's oil production has reached 1.069 million barrels per day, a Libyan oil source told Reuters, above a high reached earlier this month.
In the United States, rig counts were up to 764 in the latest week, from 371 rigs a year ago.
The executive chairman of energy services company Halliburton said he expected a US rig count above 1,000 by year end, but that about 800 to 900 rigs was more sustainable in the medium term.
"Today, rig count growth is showing signs of plateauing, and customers are tapping the brakes," said Dave Lesar. "This tapping of the brakes is happening all over the place in North America."
Still, oil prices remain under pressure, said Tony Headrick, energy market analyst at CHS Hedging LLC in Inver Grove Heights, Minnesota.
"The upside is limited because as we move towards $50 that gives US producers an incentive to hedge for future production," he said. "It all leads to a neutral market, give or take $40-$45 dollars per barrel."