Global benchmark Brent crude was up 2.2% at $96.70 (£72.18), while US-traded West Texas Intermediate was 2.8% higher at $96.90.
Oil prices remain far higher than they were before the war started on 28 February.
The cost of drude has moved higher due to suggestions that talks between Iran and the US were “still fragile”, said OCBC bank strategist Sim Moh Siong.
The flow of energy shipments through the Strait of Hormuz will be the market’s key focus in the days ahead, he added.
There is also uncertainty over how Tehran plans to oversee the movement of ships, Sim said.
Traders are watching for any changes to the supply of oil, while the relationship between Iran and the US is “obviously fragile”, Danny Price from consultancy Frontier Economics.
Given that some damaged oil and gas facilities will take time to fix, it is likely that prices will remain higher for at least a year, he added.