Russia said on Monday it might support an extension of OPEC-led supply cuts that have been in place since January, while equities rose after China eased financing rules to stem an economic downturn, giving oil a lift.
Brent crude, the global benchmark, rose 1 cent to $62.30 a barrel at 0849 GMT. US West Texas Intermediate was up 40 cents at $53.66.
"The odds are on a full agreement and co-operation between the two producers' groups," said Tamas Varga of oil broker PVM, referring to prolonged supply curbs by OPEC and its allies.
Nonetheless, "even planned and unintentional supply restrictions of more than 4 million barrels per day (bpd) have not been able to support prices as economic considerations took over in the last two weeks," he added.
The price of Brent is down almost 20pc from its 2019, peak above $75 a barrel in April, pressured by an economic downturn that has started to impact oil demand.
The Organization of the Petroleum Exporting Countries (OPEC) and some allies including Russia, known collectively as OPEC+, have been withholding supplies since the start of the year to prop up prices.
OPEC+ is due to meet in late June or early July to decide whether to extend the pact.
Russia's comments on Monday, and remarks last week from Saudi Arabia, bolstered expectations the deal will be renewed.
While the talk of prolonged supply restraint is supporting prices, concern about slowing demand and economic growth has had a bigger impact on sentiment.
"It is proving hard work papering over a suite of rather less supportive data being digested by the market," said analysts at JBC Energy in Vienna.
Analysts expect fuel consumption to stutter along with the global economy.
Energy consultancy FGE said global crude demand growth could drop below 1 million barrels per day (bpd) in 2019, from the 1.3 to 1.4 million bpd expected previously.
OPEC+ has been trying to stop inventories building up and the latest weekly reports from the United States are expected to show a small, 500,000-barrel decline in stocks.
Six analysts polled by Reuters estimated that crude inventories fell 500,000 barrels in the week to June 7. The American Petroleum Institute (API), an industry group, issues its report at 2030 GMT.