Brent crude oil futures rose 87 cents, or 1%, to $85.73 a barrel by 0111 GMT, the highest price since October 2018.
U.S. West Texas Intermediate (WTI) crude futures climbed $1.12, or 1.4%, to $83.40 a barrel, highest since October 2014.
Both contracts rose by at least 3% last week.
“Easing restrictions around the world are likely to help the recovery in fuel consumption,” analysts from ANZ bank said in a note on Monday.
“The jet fuel market was buoyed by news that the U.S. will open its borders to vaccinated foreign travellers next month. Similar moves in Australia and across Asia followed.”
They added that gas-to-oil switching for power generation alone could boost demand by as much as 450,000 barrels per day in the fourth quarter.
Still, supply could also increase from the United States, where energy firms last week added oil and natural gas rigs for a sixth week in a row as soaring crude prices prompted drillers to return to the wellpad.
The U.S. oil and gas rig count, an early indicator of future output, rose 10 to 543 in the week to Oct. 15, its highest since April 2020, energy services firm Baker Hughes Co said last week.
China’s economy, meanwhile, likely grew at the slowest pace in a year in the third quarter, hurt by power shortages, supply bottlenecks and sporadic COVID-19 outbreaks.
The world’s second-largest oil consumer issued a new batch of oil import quotas for independent refiners for 2021 that show total annual allowances were lower than last year, a first reduction of import permits since these firms were allowed into the market in 2015.