Speaking at an anti-corruption event in London, Buhari said he was more interested in the return of stolen assets held in British banks.
Cameron made the unguarded comments in a conversation with the Queen.
He is hosting an international anti-corruption summit on Thursday.
Buhari’s address at the anti-corruption event at the Commonwealth Secretariat in London followed a statement from his office on Wednesday, saying that he had been “deeply shocked and embarrassed” by Cameron’s remarks.
Asked if Nigeria was “fantastically corrupt”, in an echo of the prime minister’s comments, Buhari responded: “Yes.”
Nigeria was ranked 136 out of 167 countries in Transparency International’s 2015 Corruption Perceptions Index.
Two recent cases have illustrated the astonishing scale of corruption facing the country.
And in March, an official audit found that Nigeria’s state-owned oil company had failed to pay the government $16bn in a suspected fraud.
In his speech, the Nigerian leader described corruption as a “hydra-headed monster” which threatened the security of countries and “does not differentiate between developed and developing countries”.
He said corruption in Nigeria was endemic and his government was committed to fighting it.
Buhari praised the UK government for its help in efforts to repatriate stolen funds held in the UK.
He cited the case of disgraced Nigerian state governor Diepreye Alamieyeseigha, who fled the UK disguised as a woman while on bail for corruption charges.
British police found £1m ($1.8m) – worth of cash in his London home in 2005 and subsequently charged him with laundering a total of £1.8m.
“What would I do with an apology? I need something tangible,” Buhari said, referring to efforts to recover the money.
The UK government will host world and business leaders at the summit on Thursday in London, aiming to “galvanize a global response to tackle corruption”.
Speaking ahead of the summit, Cameron said: “For too long there has been a taboo about tackling this issue head-on.
“The summit will change that. Together we will push the fight against corruption to the top of the international agenda where it belongs.”
Anti-corruption watchdog Transparency International has criticized Cameron’s comments, accusing the UK of being part of the problem by “providing a safe haven for corrupt assets” at home and in its overseas territories.
Buhari echoed these concerns in his address, quoting from a previous study into corruption in the country’s oil sector.
“Nigerian crude oil is being stolen on an industrial scale and exported, with the proceeds laundered through world financial centers by transnational organized criminals,” he said.
(Source: BBC News)