In a 16-page state of the union address released on Sunday, Obasanjo expressed concern that Nigeria's "diligent practice of democracy" was being threatened with Buhari's high-handedness.
"What is happening under Buhari's watch can be likened to what we witnessed under Gen. Sani Abacha in many ways," he said.
He accused Buhari's government of failure, incompetence, divisiveness, nepotism, and the encouragement and condonation of corruption.
He also accused the president of hatching a plot to rig the February 16 presidential election, and called on Nigerians to "keep an eye on the unfolding anti-democratic agenda of President Muhammadu Buhari".
In response, the presidency accused the former president of being jealous of the current president "because President Buhari has more esteem than him".
Obasanjo fired back, calling the president "sick in the spirit, body and soul".
The National Council of State meeting involves past presidents and heads of state, Chief Justices of Nigeria (CJN), the leadership of the National Assembly, state governors, serving ministers and others.
Former presidents and military heads of state present at Tuesday's meeting were Obasanjo, Ernest Shonekan, Abdulsalami Abubakar, and Goodluck Jonathan. Yakubu Gowon and Ibrahim Babangida were absent.
Vice President, Yemi Osinbajo, Senate President, Bukola Saraki, and state governors of Osun, Kebbi, Zamfara, Plateau, Ebonyi, Adamawa, Edo, Lagos, Niger, Borno, Ogun, Ekiti, and Kogi were present at the meeting