Crude markets were also supported in the wake of data that showed South Korea did not import any oil from Iran in September for the first time in six years, before U.S. sanctions against the Middle Eastern country take effect in November.
Brent crude were up 25 cents at $80.68 a barrel by 2:28 p.m. ET. U.S. crude futures ended Monday's session up 44 cents to $71.78 a barrel.
Last week, both contracts fell by more than 4 percent as U.S. stock markets tumbled.
Rising geopolitical tension between the U.S., the world's top oil consumer, and Saudi Arabia, one of the biggest oil producers supported prices on Monday.
U.S. President Donald Trump threatened "severe punishment" if it is found that Khashoggi was killed in the consulate.
Saudi Arabia said it would retaliate to any action against it over the Khashoggi case, state news agency SPA reported on Sunday, quoting an official source. This comes at a critical time for global oil markets, which are bracing for U.S. sanctions against Iran due to come into force Nov. 4.
The United States is still aiming to cut Iran's oil sales to zero, Washington's special envoy for Iran said on Monday.
South Korea in September stopped importing Iranian oil for the first time in years.
"South Korea's move to stop Iran oil imports is giving the market confidence on prices," said Chen Kai, head of research at brokerage Shengda Futures.
Other producers are aiming to boost production amid falling Iranian exports, with Iraq planning to increase oil exports from its southern ports to 4 millions barrels per day (bpd) in the first quarter of 2019.
However, some risk premium was taken out of the market when Trump on Monday raised the possibility that "rogue killers" could have been responsible for Khashoggi's disappearance.
Also exerting downward pressure on prices, Friday's monthly report from the International Energy Agency said the market looked "adequately supplied for now" and cut its forecasts for world oil demand growth this year and next.
OPEC, Russia and other oil producers, such as U.S. shale companies, had increased production sharply since May, the IEA said, raising world crude output by 1.4 million bpd.
The secretary general of the Organization of the Petroleum Exporting Countries last week said that the group saw the oil market as well supplied and that it was wary of creating a glut next year.