Akram had claimed that white people were dominating cricketing affairs in the ICC and that Asian cricketers were being neglected.
But Rawalpindi-born Mani dismissed Akram's views as ill-informed.
"It is a great disappointment to see this former great player, particularly as he is from my own homeland, make such ill-informed, offensive and inaccurate comments," said Mani, who was appointed ICC president in 2003.
"As a Pakistani I am honoured by the privilege given to me to lead the ICC in carrying out its responsibility to act without fear or favour to any nation.
"The reality is that what Wasim has alleged is offensive not just to me but to everybody involved with the ICC - the directors, the umpires and referees, the staff and the many former great players from across the cricketing world, including many from Asia, who are involved with the ICC through its Cricket Committee," he said on Sunday.
Mani, a chartered accountant by profession, quoted the examples of former Indian captain Sunil Gavaskar and former South African vice-captain David Richardson, who are working for the ICC.
"With former Sir Lankan captain Ranjan Madugalle and Sri Lankan player Roshan Mahanama amongst the Emirates Elite Panel of Referees we have access to some outstanding cricketing people to deal with cricket issues," he said.
"The views of the Asian region are well represented," insisted Mani.
"In reality the ICC today is a multi-cultural body that reflects and embraces the diversity of the cricket world. This is reflected at the Board table, at all levels of the administration and in the critical operational areas of the Cricket Committee, umpiring and refereeing and anti-corruption."
Akram had branded the ICC as "a forum for white cricketers".
He said: "Mani may be a Pakistani but he has never played cricket and never been associated with Pakistan or India or Bangladesh. He has never watched a first-class game.
"My objection is that why players like Imran Khan and Kapil Dev do not get the top job in ICC? But people from Australia and England - all these one-Test wonders - get the job. We have the passion, money and the crowds. But nobody from India, Pakistan or Sri Lanka ever gets the top job in ICC."