The kidnapping last week of six oil workers, including two Germans, in Opec-member Nigeria also contributed to Monday's momentum.
Opec President Shaikh Ahmed Fahd Al Ahmed Al Sabah said on Monday he would consult oil ministers in the cartel's member countries on a 500,000 barrel per day rise in the group's output ceiling if prices did not fall.
The Organisation of Petroleum Exporting Countries (Opec) agreed last week to raise its production ceiling by 500,000 barrels a day to 28 million barrels, but that failed to soothe the market because its members had already been exceeding that level.
"We have been expecting prices to come down for a while; but this is clearly not the case. The rally is definitely sustained by demand in the United States posting a 3% yearly growth, which is seen as extremely strong," said Deborah White, energy analyst with SG Securities in Paris.
"People are trying to push prices through $60," she added.
Al Sabah said he would start consultations on another increase on Friday if prices held to current levels, a move initially agreed upon at last week's Opec meeting in Vienna.
A decision on an output increase must have unanimous support within the 11-member group for it to take effect.
"We have been expecting prices to come down for a while, but this is clearly not the case. The rally is definitely sustained by gasoline demand in the United States posting a 3% yearly growth, which is seen as extremely strong"
SG Securities energy analyst
Including Iraq, which is not bound by the quota system, Opec is pumping close to 30 million barrels a day, or about 35% of global demand.
Light sweet crude for July delivery gained 35 cents to $58.82 by afternoon in Europe in electronic trading on the New York Mercantile Exchange. Earlier, crude oil futures hit a record intraday high of $59.23 a barrel.
Heating oil rose a cent and a half to $1.6660 a gallon (3.8 litres), while unleaded petrol futures were up less than half a cent to $1.6505 a gallon.
Brent for August delivery broke the $57.65 per barrel peak it reached last April to set a new high at $58.58 on Monday on London's International Petroleum Exchange. It later fell back a bit to $58.30 a barrel, up 54 cents.
Oil workers in Norway, the world's third-largest exporter, could begin a strike as soon as early Wednesday in a salary dispute that could cut a third from the country's daily output of three million barrels.
On Friday, crude climbed as high as $58.60 per barrel before settling at $58.47, an increase of $1.89 on the New York Mercantile Exchange. That topped the exchange's previous intra-day high of $58.28 set on 4 April.
While Nymex oil futures are more than 50% higher than a year ago, they are still well below the inflation-adjusted high above $90 a barrel set in 1980.
The United States is the world's
biggest consumer of oil
"Bulls believe the only thing that can cool the market is an erosion in demand but, so far, there are no signs of this," said Energyintel analyst Matt Piotrowski.
"They also focus on Opec's recent meeting as reinforcing the belief that the organisation cannot cool prices."
Analysts said unlike the record prices last year, which were driven largely by concern over geopolitical events in oil-producing countries such as Nigeria, Saudi Arabia, Iraq and Venezuela, this year's trend had more to do with
speculative buying, continued supply fears and limited excess production capacity.
"This year we've had a confluence of factors driving up this rally: first, more hedge funds are allocating money to the red-hot oil markets; second, demand is outstripping supply; and third, capacity is tight in refineries and Opec production facilities," said Victor Shum, energy analyst at Texas-based Purvin & Getz.
"The oil market is prone to price spikes because of capacity tightness, and this attracts the speculators, who tend to buy on momentum," Shum said.
Analysts also said demand for distillates in the summer - petrol for holidaying Americans and diesel for generators of small businesses in China when power shortages occur - keep the market on edge.
"This year we've had a confluence of factors driving up this rally: first, more hedge funds are allocating money to the red-hot oil markets; second, demand is outstripping supply; and third, capacity is tight in refineries and OPEC production facilities"
Purvin & Getz energy analyst
"We saw last week's expectation being built that US refineries would struggle to meet the demand of the driving season. This is likely to provide support for the coming week," said ANZ Bank energy analyst Daniel Hynes in Melbourne, Australia.
Hynes also said crude's rise was partly a reaction to the kidnapping of two German and four Nigerian Shell sub-contractors who had been seized by gunmen on Wednesday.
They were released on Saturday. Nigeria exports about 2.5 million barrels of oil daily, making it the world's seventh-leading exporter and the fifth-biggest source of US oil imports.