The guests had moved with him from the Eagles Square where he and Vice-President Yemi Osinbajo had earlier taken their oaths of office to the Villa for a luncheon.
Buhari, however, left the venue midway into the programme while his guests were taking their lunch.
After waiting for a while for the President to return, organisers decided to invite Osinbajo to make remarks on behalf of Buhari.
The crest of the Commander-in-Chief was quickly removed from the podium to enable the vice-president make use of it.
Osinbajo, in his remarks, apologised to the guests for the President’s absence.
He explained that he left in order to take part in Jumat prayers.
The President did not return to the venue before the programme ended.
The vice-president thanked the African leaders for attending the inauguration.
He said the inauguration marked the beginning of the change Nigerians had been yearning for.
Osinbajo said Nigeria, under the watch of the new administration, would remain committed to ensuring equality among the citizens.
He said, “On behalf of the people of Nigeria and most especially on behalf of the President, I thank you and wish you safe journey back home.”
The vice-president later saw the African leaders off on behalf of the President before being driven away in his official car.
African leaders, who graced the event included those of South Africa, Liberia and and Guinea, among others.
All Progressives Congress chiefs such as Governor Adams Oshiomhole of Edo State; former Governor Kayode Fayemi of Ekiti State; former Governor Timipre Sylvia of Bayelsa State; Senator Oloruninbe Mamora; and Mr. Nda Isaiah among others attended the event.