In morning trade, New York's main oil futures contract, light sweet crude for June delivery, was up 19 cents to $127.24 per barrel.
The benchmark futures contract closed at $127.05 a barrel yesterday at the New York Mercantile Exchange, off its all-time peak of $127.82 struck on Friday.
London's Brent crude contract for June rose 29 cents to $125.35 a barrel. It hit a record $126.34 on Friday.
Amid rocketing prices, Saudi Arabia increased oil output by 300,000 barrels per day to meet demand and compensate for lower output from other producers, Saudi Oil Minister Ali al-Nuaimi said on Friday.
Saudi Arabia, the world's biggest producer of crude, said that by June it would be producing 9.45 million barrels of oil per day.
But Victor Shum, an analyst with energy consultancy Purvin and Gertz in Singapore, said there were no signs prices were cooling down following Saudi Arabia's decision.
Prices are expected to remain high because of tight supplies amid persistently robust global demand, he said.
"The tightness in the market continues to empower investors to ply money into oil... So (prices) are likely to test the psychological level of $130 in the near term," Shum said.
"There are no signs of any major correction (in prices)". Saudi Arabia's Nuaimi had earlier reiterated the view of the Organisation of Petroleum Exporting Countries (OPEC) that global oil supply was balanced with demand.
