The 72-year-old head of state, in Washington for talks with US officials, alleged that 250,000 barrels of crude were being stolen every day, with the profits going into individual bank accounts.
Buhari, a former military ruler, has carved a reputation as a no-nonsense crusader against graft and has vowed the corrupt and corruption “will have no place” in his government.
He told an audience at the Nigerian Embassy in Washington on Tuesday evening that the United States and other countries “are helping us to trace such accounts now”.
“We will ask that such accounts be frozen and prosecute the persons. The amount involved is mind-boggling. Some former ministers were selling about one million barrels per day,” he alleged.
“I assure you that we will trace and repatriate such money and use the documents to prosecute them,” he said, according to a statement from his spokesman Femi Adesina.
Buhari, in power since May 29, has pinpointed the state-run oil firm as a key culprit in a pervasive culture of corruption, sacked the entire board and ordered an investigation into its finances.
Last year, a political row ensued between his predecessor Goodluck Jonathan and the governor of the Central Bank of Nigeria, who alleged $20 billion of oil revenue had gone missing.
The governor, Lamido Sanusi, was later sacked.
Buhari has accused the previous administration of leaving the treasury “virtually empty” and is grappling with how to turn around an oil-dependent economy hit by falling global crude prices.
The focus of looted state revenue has until now been focused on accounts linked to the former military ruler Sani Abacha, who ruled with an iron fist from 1993 until his death in 1998.
Abacha is suspected to have looted the public purse of some $2.2 billion, squirreling away the money in European accounts.
In March last year, the United States said it had ordered a freeze on $458 million in assets stolen by Abacha and his accomplices, calling him “one of the most notorious kleptocrats in memory”.
Since then, Switzerland has said it will return some $380 million seized in Luxembourg in 2006, after a deal in which Nigeria accepted to drop a case against Abacha’s son.