Obasanjo returned the fireworks on Monday, telling the BBC: "Buhari is sick in the spirit, body and mind."
"Obasanjo is expired. Ota is enough a place to keep quiet,” he said.
Obasanjo on Sunday criticised Buhari, accusing him of plotting to rig the elections.
Bishop Kukah also explained how he initiated the reconciliation moves and how he worked hard to be a neutral.
"I do not have personal grudges with anyone," Mr Obasanjo said. "If you do not do well for Nigeria, you do not do well for all of us."
Obasanjo has lashed out at President Buhari for his “mediocre” performance during his latest trip to the United States.
Nobel Laureate, Prof. Wole Soyinka, has said he should be examined by a psychiatrist, if he joins the Coalition for Nigeria Movement, CNM, spear-headed by ex-President Olusegun Obasanjo.
Mr. Shittu also recently opened a South West campaign office for Mr. Buhari and his vice, Yemi Osinbajo, ahead 2019 election in Ibadan Oyo state.