Brent crude futures rose 21 cents, or 0.3%, to US$83.54 a barrel by 0810 GMT while U.S. West Texas Intermediate (WTI) crude futures were up 1 cent at US$78.49
Israel withdrew forces from the southern Gaza city of Khan Younis over the weekend, bringing its troop levels in the enclave to one of the lowest levels since the war with Hamas began last October.
U.S. crude and Brent gained more than 4% last week as tensions mounted between Israel and Iran.
Oil prices fell in early Asian trade on Monday after Israel said it had “concluded” a series of strikes in southern Gaza, slightly easing concerns about supply from the Middle East.
Crude oil prices have ticked up over 2% in the aftermath of the rejection of a ceasefire in Gaza.
Israeli Prime Minister Benjamin Netanyahu vowed to continue the war until “victory”.
The rejection of a ceasefire deal comes a day after the U.S. launched one of a series of retaliatory strikes following the death of three American soldiers in Jordan.
Shipping disruptions across the Red Sea threaten global trade after major shippers, such as Maersk and others, have rerouted vessels.
As of Monday, QatarEnergy, one of the world’s largest LNG exporters has stopped shipping cargoes through the Red Sea.
Possible delays or disruptions of LNG shipments from Qatar are not a concern to European traders yet.