Bashir had been attending an African Union (AU) health summit which was due to end on Tuesday.
"He has left. He left in the afternoon [on Monday]," Mohammed Moiz, said spokesperson for the Sudanese embassy in Nigeria on Tuesday. He said Bashir had left due to another engagement.
The embassy spokesperson said Bashir, who had arrived on Sunday, returned to Khartoum, but gave no further details on the other engagement.
Nigeria's presidency defended welcoming Bashir to the country for the summit scheduled for Monday and Tuesday despite war crimes charges against him, saying it cannot interfere in AU affairs.
The Hague-based International Criminal Court (ICC) in 2009 and 2010 issued two warrants against Bashir for war crimes, crimes against humanity and genocide over the conflict in Sudan's Darfur region.
Since Nigeria is a member of the ICC, it technically has a legal obligation to arrest suspects wanted by the court.
Activists harshly criticise Bashir
Some African Union members and officials have criticised the Bashir indictments, and the body has passed a resolution calling on members not to cooperate with the warrants.
Rights activists harshly criticised Bashir's visit and said they were planning to go to court to try to force Nigeria to arrest him.
Bashir has previously visited ICC member states, including Chad, Djibouti and Kenya, but countries like South Africa and Botswana have ensured he stay away.
Human Rights Watch said the AU resolution to ignore the warrants has "no bearing on Nigeria's obligations as an ICC member".
Hosting Bashir is an "affront to victims" of the Darfur conflict, said Elise Keppler of the International Justice Programmee at Human Rights Watch.
The court has been accused by some of unfairly targeting Africans, while others have argued that the arrest warrants against Bashir complicate peace efforts.
'Damaging legacy of colonialism'
Rights activists said that the vast majority of current investigations came about because the governments where the crimes were committed asked for the court's involvement or the UN Security Council referred the situation due to the gravity of the crimes.
"How can the court be targeting if they are responding to direct requests from governments affected or the council?" Keppler said.
She added that "even though the claim of targeting flies in the face of the facts, it continues to have great resonance in public debate likely due to the damaging legacy of colonialism, and it is being leveraged and manipulated to undercut efforts to give access of African victims to justice".
Government forces and local Arab militias were pitted against rebels drawn mainly from non-Arab populations in the conflict in the Darfur region.
In 2008, the United Nations estimated that 300 000 people had died because of the conflict but Khartoum disputes the figure. – AFP