He said his talks on Saturday with King Abdullah had focused on the link between the soaring world crude prices and the worsening food crisis as well as climate change.
"He acknowleged that the current oil prices are abnormally high due to speculative factors and some other national government policies," Ban said before leaving Jeddah.
"He is willing to do what he can to [bring] the price of oil to adequate levels."
The Saudis "seem to be considering very seriously how they can address this issue by increasing production", Ban said.
"I expect that they will take some concrete measures."
While reaping record profits, the Saudis are concerned record prices might dampen economic growth and lead to lower oil demand, as is the case in the United States and other developed countries, The New York Times reported.
It said the high prices are also making alternative fuels more viable, threatening the long-term prospects of the oil-based economy of Saudi Arabia, which is currently pumping 9.45 million barrels a day.
Oil prices - which have witnessed a fivefold jump since 2003 - fell back on Friday to just under $135 a barrel.