The new president said on Tuesday that the country’s treasury was “virtually empty”.
He vowed to recover billions of dollars “stolen” under previous administrations.
The president won elections in March on a promise to tackle corruption, seen as one of the country’s biggest problems.
Nigeria is Africa’s biggest oil producer but much of the revenue is said to be stolen.
“The days of impunity and lack of accountability are over,” he told a meeting of state governors on Tuesday.
He said Nigeria would get the “facts and the figures to help us recover our stolen funds in foreign countries,” over the next three months.
He did not specify which other countries had agreed to help recover the money.
In an earlier briefing with journalists, he said it was a “disgrace” that some government workers had not been paid for months.
Vice-President Yemi Osinbajo estimates that Nigeria’s debts stand at about $60bn (£38bn).
However, former Finance Minister Ngozi Okonjo-Iweala has rejected the claim, saying the debt was much lower, an international news agency reports.
Mr Buhari’s election victory ending 16 years of rule by the Peoples Democratic Party.
It was the first time an opposition candidate has won a presidential election in Nigeria.