Activists had filed suit in Nigeria's Federal High Court to force the arrest of Bashir, charged by the International Criminal Court on accusations of war crimes and genocide in Sudan's Darfur region, Voice of America reported Tuesday.
Sudanese Embassy officials said Bashir's departure wasn't related to the calls for his arrest.
He was in Abuja for an African Union conference on AIDS, Sudanese officials said.
A Nigerian presidential spokesman indicated authorities would not arrest Bashir, VOA said. The spokesman said Bashir was invited by the African Union, which has backed his refusal to surrender to the ICC or recognize the court's authority.
The ICC, sitting in The Hague, Netherlands, indicted Bashir on charges of war crimes, crimes against humanity and genocide in Darfur. He is accused of orchestrating crimes including murder, rape and the slaughter of civilians in the region, where anti-Bashir rebel groups have been fighting the government since 2003.
Bashir has denied the charges and defied the ICC's arrest warrant. When he travels, he only visits countries that aren't members of the ICC or have guaranteed his safety.