Saudi Arabia's King Abdullah announced on Sunday that his country had increased output to 9.7 million barrels a day as he opened a summit on the soaring international price of crude in the Saudi city of Jeddah involving producers and consumers.
However the market had already expected the formal announcement after the kingdom's London embassy had released a statement last Thursday that outlined a plan to increase output by 200,000 barrels a day.
Prices also shot higher on Monday after militants blew up a pipeline in Nigeria over the weekend, traders said.
At about 1545 GMT, New York's main oil futures contract, light sweet crude for August delivery, was up 79 cents to 136.13 dollars per barrel, off earlier highs of above 137.
Brent North Sea crude for August jumped 1.27 dollars to 136.13 dollars.
"The debate regarding 'high' oil prices is no less transparent today than it was on Friday," said Stephen Schork, editor of the Schork Report energy newsletter.
"We fear that since the Saudis did not give this market a reason to sell, the market will interpret that as a reason to buy."
The White House on Monday welcomed Saudi Arabia's decision to increase its oil output but expressed skepticism that the move would have much of an impact on sky-high US gasoline prices. "We certainly think that it's welcome that Saudi Arabia will further increase their production," spokeswoman Dana Perino told reporters.
"But we also believe that the fundamental issue of supply and demand continues to rule on this predicament that we are in in our country," said Perino. "We will have to see."
Meanwhile in Nigeria, militants attacked a key Chevron oil supply pipeline over the weekend in the latest operation targeting Nigeria's oil industry, company and military sources said.
The US oil giant was forced to shut down activities after the attack in the volatile Niger Delta, halting output by 120,000 barrels per day, an industry source said.
The Anglo-Dutch oil giant Shell has also said it cannot promise to deliver 225,000 barrels per day for June and July following an unprecedented raid on its offshore Bonga oilfield.
Unrest in the Niger Delta has cut total oil production in one of Africa's biggest producers by a quarter over the past two years.
One week ago, New York crude struck a record high of 139.89 dollars per barrel. Brent North Sea crude hit an all-time peak of 139.32 dollars on June 16.
While OPEC members blame soaring prices on speculative buying from investors, consumers say that producers need to pump more oil.
Crude futures are also being supported by a weak dollar, which makes oil cheaper for foreign buyers, according to analysts.
Saudi Arabia is the world's lynchpin oil producer and the largest in the Organisation of the Petroleum Exporting Countries (OPEC) cartel, which pumps about 40 percent of the world's crude.