Funds were keen to shift their money into the oil market after seeing U.S. crude rise about 13 percent since the start of the month.
U.S. crude for June delivery CLc1 rose as far as $124.70, surpassing the previous record of $124.61 hit on Thursday.
By 6:25 a.m. British time, the June crude contract was $124.55 a barrel on the Globex electronic trading platform, up 86 cents, or 0.7 percent.
London Brent crude LCOc1 rose 85 cents to $123.69 per barrel.
"Funds are pouring into the crude market as prices have been performing extremely well," said Tatsuo Kageyama, analyst at Kanetsu Asset Management in Tokyo.
"Lingering geopolitical fears and high heating oil prices are helping the market, but the speed of the rise is too fast."
Gains in U.S. crude picked up momentum after distillate stocks in the United States, including heating oil, fell.
The U.S. Energy Information Administration (EIA) said on Wednesday domestic distillate stocks, which include heating oil and diesel, fell 100,000 barrels last week, to 105.7 million barrels, against forecasts for an 800,000-barrel rise.
NYMEX June heating oil HOM8 was up 0.67 cents at $3.5164 on Globex, after reaching a record high of $3.5310 a gallon the previous day.
"I'm not particularly surprised by the speed of the rise in crude. There are many market bulls hoping for prices to rise heading into the summer," said Tetsu Emori, fund manager at Astmax Co Ltd in Tokyo.
Yet, the recent recovery in the dollar against the euro was negative for oil, traders said.
Producers were also ready to provide more supplies.
World oil markets have enough supply now, but the Organization of the Petroleum Exporting Countries is willing to pump more if needed to keep pace with demand, Abdullah al-Badri, the group's secretary-general, said on Thursday.
OPEC exports, excluding from Angola and Ecuador, will rise by 220,000 barrels per day (bpd) in the four weeks to May 24 on Asian demand and a recovery in Nigerian supplies after a strike that crippled output, said British consultancy Oil Movements.
The euro was little changed against the dollar on Friday after rebounding from a two-month low on reduced expectations for European Central Bank rate cuts.
"It's basically crude oil and grains in commodities which are doing well and funds are shifting in those markets. But the strength of the dollar is not necessarily positive for oil," Kanetsu's Kageyama said.
Traders will be watching the release later on Friday of U.S. international trade data for March (1:30 p.m. British time) and the Economic Cycle Research Institute weekly index at (3:30 p.m. British time) for potential price guidance.
