He vowed to recover billions of dollars "stolen" under previous administrations.
Mr Buhari held talks with state governors over the lack of money to pay government workers their salaries.
He and his All Progressives Congress won elections in March, ending some 16 years of rule by the Peoples Democratic Party.
He was sworn in less than four weeks ago, taking over from Goodluck Jonathan, who had been in office since 2010.
"The days of impunity and lack of accountability are over," he told state governors.
"The next three months may be hard, but billions of dollars can be recovered, and we will do our best," he added.
In an earlier briefing with journalists, he said it was a "disgrace" that government workers had not been paid for months.
African news updates
"This bad management we find ourselves in - we really need your help to protect us from people before they march on us," he said.
Vice-President Yemi Osinbajo estimates that Nigeria's debts stand at about $60bn (Â£38bn).
However, former Finance Minister Ngozi Okonjo-Iweala has rejected the claim, saying the debt was much lower and most of it was incurred by states, rather than the federal government, AFP news agency reports.
The president won the elections on a promise to tackle corruption, and to lead Nigeria to greater prosperity.
Nigeria is Africa's biggest oil producer, but most of its citizens are poor.

The A547 at Meliden, between Rhuddlan and Prestatyn, was closed after 14:00 BST on Saturday after the collision.
The child was taken to hospital, with the extent of his injuries not yet known.
Police confirmed traffic had resumed on the road after 16:00 BST.

British and Irish Lion North, 23, has signed a new contract with Northampton Saints in England's Premiership.
The 23-year-old's previous deal was due to expire next summer and he had been linked with a return to Wales.
"We'd all want to see our best players playing in Wales," Davies said. "Why would we want it any different?"
Davies was Scarlets chief executive when North left them for Saints in 2013, and moved to the Pro Rugby Wales role in September 2014.
He would like to see players such as North back in Wales to offer a "return on investment to the regions that have developed them" as well as to reward fans and to inspire younger players.
Davies added: "From the national squad's point of view, the coaches are very clear that they fundamentally believe that it is a better environment in terms of player management for the players to be playing in Wales.
"They can manage them better in conjunction with the regions."
North, capped 55 times by Wales and also a 2013 Lions tourist in Australia, has appeared 42 times for Saints.
There was speculation he might emulate Wales team-mate and former regional colleague Jonathan Davies, who will return to Scarlets from Clermont Auvergne on a Welsh Rugby Union dual contract next season.
Former Wales centre Tom Shanklin is also disappointed North will remain in England.
"It's probably good for him personally because he's at a very good club and in a very good league," Shanklin told Scrum V Radio.
"But I want to see all the Welsh players back. That's going to strengthen our league and strengthen our product on the field.
"We had some great news Jon Davies is coming back so it's a bit of a shame."

The Dow Jones industrial average slipped 5.23 points to 16,995.13.
The S&P 500 gained 0.31 points to 1,989.57, while the tech-focused Nasdaq index fell 12.22 points to 4,662.16.
US markets mirrored those in Europe after ECB head Mario Draghi said the bank would expand stimulus measures, but did not expect further rate cuts.
Shares in mobile payment company Square fell 6.1%. The company reported on Wednesday that it had seen growth in payment volume over the fourth quarter, but also increasing operating expenses.
Dollar General shares rose 10.7% after the company reported profits of $376m. Its discount competitor Dollar Tree saw its share price rise 4%.
Nigeria's treasury is "virtually empty", President Muhammadu Buhari has said.
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A Denbighshire road has been reopened after a boy was hit by a car, North Wales Police says.
[NEXT_CONCEPT]
Wales wing George North's decision not to return to a Welsh region is a disappointment, says Rugby Wales chief executive Mark Davies.
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(Close): US stocks finished mostly lower following a turbulent trading day and an announcement of new stimulus from the European Central Bank.