According to Nigerian authorities, the evacuation plan is for more than 3,500 nationals, but their total number could be greater.
Many of the Nigerians in Sudan are students.
Egyptian authorities on Monday agreed to let an earlier group of Nigerian evacuees cross after President Muhammadu Buhari intervened, the Nigerians in Disapora Commission said in a statement on Twitter.
Nigeria's National Emergency Management Agency (NEMA) confirmed the group was already in Egypt but could not give details on when they would be flown home.
Another 20 buses prepared to evacuate hundreds more Nigerians were still blocked in Sudan.
That convoy would no longer travel to Egypt, but to Port Sudan, a city located on the Red Sea, 675 kilometers from Khartoum, from where they should then be flown back to Nigeria, NEMA spokesman Manzo Ezekiel told AFP on Tuesday.
Sudan was plunged into fighting on April 15 between two generals who have been in charge of the country since a military coup in 2021.
Army chief Abdel Fattah al-Burhan and Rapid Support Forces (RSF) paramilitary commander Mohamed Hamdan Dagalo had agreed to extend a three-day ceasefire.
But air raids, shooting and explosions continued to shake Khartoum, the capital, despite that truce.