The official, who gave no further details, spoke Wednesday on condition of anonymity because he was not authorized to brief the media.
This is while the Egyptian liberal opposition leader Mohamed ElBaradei also met al-Sisi on Wednesday, two political sources said.
The heads of state Islamic institute, Al-Azhar, and the Egyptian Coptic Church also joined the meeting, a government source said.
Political sources said two members of the "Tamarud - Rebel!" youth group that is leading the anti-Mursi protests also attended, as did members of the Muslim fundamentalist Nour Party.
Al-Azhar's Grand Sheikh, Ahmed al-Tayeb, endorsed the army's position, calling on political leaders to heed anti-government protesters. Pope Tawadros, spiritual leader of some 10 percent of Egypt's 84 million people, tweeted his blessing for the anti-Mursi revolt on Tuesday.
ElBaradei was chosen to represent the opposition National Salvation Front coalition and youth groups leading anti-Mursi street protests to negotiate with the army on their behalf.
This is while embattled President Mohammed Morsi vowed late Tuesday to stay in office and called on the military to withdraw its ultimatum, which expires later Wednesday.
The military says if no agreement is reached, it will intervene to implement a political road map of its own to shepherd Egypt out of its crisis.
Millions have been taking to the streets since Sunday to call on Morsi to step down.