The meeting is being attended by state governors and ministers who are members of the council.
It started at about 10.11am with the arrival of Osinbajo at the Council Chambers venue of meeting.
While some state governors are attending personally, some others are being res presented by their deputies.
Among those being represented by their deputies are Ayodele Fayose of Ekiti State and Nyesom Wike of Rivers State.
The governors, it was learnt, will also meet briefly with President Muhammadu Buhari after the NEC meeting.