Front-month U.S. crude futures were trading at $40.91 a barrel at 0121 GMT, up 17 cents from their last close.
Internationally traded Brent was at $44.66 a barrel, up 19 cents.
Both crude benchmarks, which lost 8 percent last week, saw high levels of activity in early trading as commodity traders looked nervously for direction following the deadly attacks in Paris on Friday.
"The big question is, given that there is so much uncertainty with the security issue if borders in Europe start to close, what economic impact could that have? That would probably be a very damaging factor," said Dominic Schnider, analyst at UBS Wealth Management in Hong Kong.
ANZ bank bank said that oil prices would remain under pressure from fundamentals as production remains high despite slowing global economic growth.
"Surprisingly, U.S. drillers are putting rigs back to work in the oil fields after more than two months. Baker Hughes reported the U.S. oil rig count gained by 2 to 574," ANZ bank said on Monday, but added that "we believe the low oil price environment will lead to a decline in drilling activity in the coming weeks."
Oil prices have dropped more than 60 percent since June last year as high production has coincided with an economic slowdown in Asia, particularly in China but also Japan, which slipped back into recession in the third quarter.
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