Brent crude was up $1.14 or 1.5% at $79.23 a barrel by 0208 GMT, having risen a third consecutive week through Friday. U.S. Oil added $1.11 or 1.5% to $75.09, its highest since July, after rising for a fifth straight week last week.
Rising gas prices as also helping drive oil higher as the liquid becomes relatively cheaper for power generation, ANZ analysts said in the note.
Caught short by the demand rebound, members of the Organization of the Petroleum Exporting Countries and their allies, known as OPEC+, have had difficulty raising output as under-investment or maintenance delays persist from the pandemic.
China's first public sale of state oil reserves has barely acted to cap gains as PetroChina and Hengli Petrochemical bought four cargoes totalling about 4.43 million barrels.
India's oil imports hit a three-month peak in August, rebounding from nearly one-year lows reached in July, as refiners in the second-biggest importer of crude stocked up in anticipation of higher demand.