"The president called on the good offices of the United States to intervene so that Nigeria will respect its international obligations," the aide said, speaking on condition of anonymity.
He said Biya made the request during talks this week with U.S. President George W. Bush's special assistant Cindy Courville, who is director for African affairs at the National Security Council.
"The normalisation of relations between Yaounde and Abuja is primordial for security in the entire Gulf of Guinea, and this cannot be done as long as Nigeria continues to occupy the Bakassi peninsula," the aide said.
Most of Bakassi is wetlands rich in fish, but the offshore area in the Gulf of Guinea contains oilfields already producing under Nigerian licences and there is potential for more discoveries, especially in deep water.
The Gulf of Guinea has seen a swathe of huge deep water oil discoveries over the last decade and could provide the United States, the world's biggest energy consumer, with a strategic supplement to its supplies from the Middle East.
Bakassi's status almost brought Nigeria and Cameroon to war in 1981. After more clashes in the 1990s, the International Court of Justice (ICJ) ruled in 2002 that Bakassi belonged to Cameroon. Nigeria was due to hand over the peninsula last September but failed to do so, citing "technical difficulties".
The handover had been opposed by some Bakassi leaders and Nigerian lawmakers who say the peninsula is home to 300,000 people who do not want to become Cameroonians. Nigeria still maintains a strong military presence in Bakassi.
United Nations officials say the number can vary from 25,000 to 250,000 as fishermen flock to the peninsula's rich waters at certain times of the year. It also says Cameroonians who fled the area when Nigeria moved in are keen to return.
Biya met Courville on Thursday.
"It is absolutely important that we resolve this issue once and for all through dialogue," the aide quoted Biya as telling Courville's eight-person delegation.
Courville told Cameroon's state television on Thursday that the Washington delegation wanted to reaffirm strong bilateral relations with Cameroon.
They also wanted "to discuss our economic engagement, and ... to look at military-to-military relationship and security not only in Cameroon, but the Gulf of Guinea," she said.
Nigerian President Olusegun Obasanjo met Bush in Washington Thursday and said they discussed oil supplies. The U.S. president has been pressing producers like Nigeria to increase output to help lower prices.