Saudi Oil Minister Ali al-Naimi made the oil pledge to Mr Ban on Sunday
Saudi Arabia will increase its oil production by 200,000 barrels a day next month in a move to meet growing world demand, the United Nations says.
The news was announced after UN Secretary General Ban Ki-Moon met Saudi Oil Minister Ali al-Naimi in Jeddah for talks on the high oil price.
Last month, the Kingdom increased its production by 300,000 barrels a day.
The country is thought to be the only oil producer with the ability to pump substantially more crude.
It argues that the current high prices are caused by speculators rather than any shortage of crude oil.
Oil prices fell by almost $2 on Friday after reports that Saudi Arabia might boost oil production. US light, sweet crude was trading at $134.86 in New York.
After an earlier meeting with the Kingdom's King Abdullah, Mr Ban said Saudi Arabia, the world's biggest oil producer, viewed current prices as "abnormally high".
The price of oil keeps on rising
"He [King Abdullah] acknowledged that the current oil prices are abnormally high due to speculative factors and some other national government policies," Mr Ban said.
"He is willing to what he can to [bring] the price of oil to adequate levels."
On Friday, the Saudi oil minister said current elevated oil prices - which hit a record high of more than $139 (£71) a barrel last week - were unjustified.
Oil minister Ali al-Naimi said a meeting of oil exporters and importers to be held in Jeddah later this month would seek a solution to the unprecedented high prices, the Saudi state news agency said.
The Kingdom is hosting an international gathering of oil producers and consumers in a week's time.