Vice President Yemi Osinbajo chaired the meeting in the absence of the 74-year-old Buhari, who has now missed the last three gatherings of senior ministers and advisers.
The devout Muslim was also absent from Friday prayers last week and failed to attend his grandson's wedding on Saturday.
His spokesman said he had undergone "a long period of treatment" for an undisclosed illness in London earlier this year and needed rest. He was working from his private residence.
Buhari has been under growing pressure to disclose his state of health since he returned from the British capital in early March after nearly two months away.
On Tuesday, prominent Nigerians and civil society activists advised him to take medical leave.
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Local media reported on Wednesday that former president Olusegun Obasanjo met other ex-military rulers Ibrahim Babangida and Abdulsalami Abubakar to discuss the situation.
Buhari's wife, Aisha, however said her husband's health was "not as bad as it's being perceived", without specifying the nature of his illness.
"He continues to carry out his responsibilities during this period," she wrote on her Twitter account on Tuesday evening.
The health of Nigeria's president has been a sensitive issue since the death in office in 2010 of Umaru Musa Yar'Adua, which sparked months of political turmoil and uncertainty.
During the 2015 election campaign, Buhari rejected opposition claims that he was seriously ill with prostate cancer and said they were a smear to show him as unfit for office.
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