Fears of US petrol shortages and rapid economic growth in China also spurred the increase.
Brent North Sea crude closed at $71.46 a barrel on Monday. That was up 89 cents from Thursday's closing level in London, and just off a new high reached earlier on Monday of $71.62.
In New York, light sweet crude for May delivery surged $1.08 dollars from Thursday to close at $70.40 a barrel, testing levels not seen since last summer.
The New York and London markets had been closed for the Good Friday holiday.
Crude prices had last set a record in New York of $70.85 on August 30, after Hurricane Katrina hammered oil production facilities in the US Gulf of Mexico region.
Iran warned Washington on Sunday against attacking its nuclear facilities, saying it had tens of thousands of would-be suicide bombers at the ready and could count on the support of militants across the region.
Alaron Trading analyst Phil Flynn said the increase in price reflected the market's concerns over Iran.
"The oil market is taking the threat seriously as Iran may have gone down the path that leads to the point of no return."
Traders worry that US-led military action would disrupt vital oil supplies from Iran, which is the world's fourth-largest producer of crude with an output of four million barrels per day.
"And Iran is not the only oil hotspot on the globe right now," Flynn said, mentioning fears for supplies from Nigeria and Venezuela. "Small disruptions can quickly escalate to big-number problems."
Concerns over US petrol supplies have also mounted after the latest department of energy report last week showed another drop in stocks heading into the summer driving season.