ICE Brent was up by 1.58% at $111.22/bbl, in late afternoon trading.
On Monday, crude futures gained $1.62, or 1.5%, to settle at $111.76 a barrel.
Key to the new records today was concern over supply disruptions. Bad weather in Mexico forced the closure of five Petroleos Mexicanos export terminals over the past week. The company is the third largest supplier of crude oil to the US.
Meanwhile Eni SpA, Italy's biggest energy company, had announced on Monday that oil plants in Nigeria had been attacked by militants leading to an output cut of up to 5,000 barrels per day.
Oil producers' cartel the Organization of Petroleum Exporting Countries (OPEC) has signalled its intention to lower production in tandem with a seasonal slowdown in demand which has also pushed prices higher.
Analysts also noted that the weak US dollar would enable crude oil to continue posting fresh highs.
"The price movement for some time has moved beyond the basic fundamentals," said MF Global's Mike Fitzpatrick. "What is remarkable to us, is the ability of market participants to completely overlook the weakening economy and oil demand that should falter as a consequence. Apparently with several refineries reporting problems recently and margins still weak, there are concerns the supply situation in the product markets may quickly tighten."
In a research note, Barclays Capital noted that while the supply disruptions will not bear a lasting influence on the oil space, "they serve as a reminder that supply disruptions accentuate price fluctuations in a context of tight fundamentals, low inventory cover and little spare production capacity."
The week on Risk.net, March 10-16 2018Receive this by email