Brent crude futures for November rose 31 cents, or 0.4%, to $72.53 a barrel by 0452 GMT, after falling 39 cents on Monday.
U.S. West Texas Intermediate crude for October was at $69.14 a barrel, down 15 cents, or 0.2%, from Friday's close, with no settlement price for Monday due to Labor Day holiday in the United States.
Demand woes grew after state oil group Saudi Aramco notified customers that it will cut October official selling prices (OSPs) for all crude grades sold to Asia by at least $1 a barrel.
The deep price cuts, a sign that consumption in the world's top-importing region remains tepid, come as lockdowns across Asia to combat the delta variant of the coronavirus have clouded the economic outlook.
Markets are also contending with a decision by the Organization of the Petroleum Exporting Countries and their allies, a grouping known as OPEC+, to raise output by 400,000 barrels per day a month between August and December.
"Brent came back as investors adjusted positions, but market sentiment remained weak due to slow demand in Asia and in the United States amid a resurgence of the pandemic," said Tetsu Emori, CEO of Emori Fund Management Inc.
"In order for WTI to move above $70 a barrel, we need some fresh positive news such as signs of subsiding infection or rising demand of jet fuels," he said.
The U.S. economy created the fewest jobs in seven months in August as hiring in the leisure and hospitality sector stalled amid a resurgence in COVID-19 infections, which weighed on demand at restaurants and hotels.
Toshitaka Tazawa, an analyst at Fujitomi Securities Co Ltd, also said that oil prices are expected to struggle to move higher as the U.S. summer driving season wanes after Labor Day weekend.
Oil prices were underpinned, however, by concerns that U.S. supply would remain limited in the wake of Hurricane Ida.
More than 80% of oil production in the Gulf of Mexico remained shut after Ida, a U.S. regulator said on Monday, more than a week after the storm made landfall and hit critical infrastructure in the region. read more
Hedge funds purchased petroleum last week at the second-fastest rate this year after Ida disrupted offshore oil wells and onshore refineries in the Gulf of Mexico.
Also providing a support, China's daily crude oil imports rose 8% in August from a month earlier, customs data showed on Tuesday, as refiners resumed purchases following the issue of new import quotas.