The president "has just been informed of the tragic deaths of several members of his All Progressives Congress (APC) party in a stampede during a presidential rally held in Port Harcourt in Rivers State," it said in a statement released late Tuesday.
Local media said panic broke out at the end of the gathering, held inside the Adokiye Amiesimaka Stadium, when crowds tried to force their way through a locked exit.
"Those from behind were pushing and putting pressure on those in front leading to some persons falling on the ground and being trampled upon," said journalist Egufe Yafugborhi of the Vanguard newspaper.
"There are others under medical attention at the Emergency Unit, so we can't force a clear figure beyond what the situation is at the moment," Kem Daniel-Elebiga told AFP.
In recent weeks, tensions have risen between the APC and Abubakar's People's Democratic Party (PDP).
The PDP has accused the government of seeking to rig the vote while the APC has said the opposition party is fomenting unrest.
Five people were killed during weekend clashes between supporters of the two main political parties in the southeast, police had confirmed on Monday.
The US, Britain and the European Union have in recent weeks publicly warned against vote-rigging and election violence, and also expressed concern over Buhari's suspension of Nigeria's top judge last month.
Nigeria's last election in 2015 was considered free and fair, but state and local elections as well as earlier presidential polls have been marred by violence and fraud allegations.
Compared to that vote, international interest in Nigeria's election has been muted as the US administration focuses on domestic issues and Britain wrestles with its impending exit from the EU.
A British colony until 1960, Nigeria is an ally of both countries which are home to large Nigerian diaspora communities.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)