Ms Sanda-Usara said the Nigerian team also invited the Saudi Minister of Hajj and Umrah to visit Nigeria.
The airline said passengers could also fly Accra-China-Accra, a new connection.
The embassy advised passengers to review all documents before departing their countries to the Kingdom.
Saudi Arabia and the U.S. have yet to confirm the resumption of talks between Sudan’s warring factions.
The no fewer than 1,070 pilgrims transported so far are out of the 4,913 pilgrims billed for the 2023 pilgrimage in Saudi Arabia.
The air strikes, explosions, and clashes could be heard in the south of Khartoum, and there was heavy shelling across the River Nile.
“We recognise the presence of other Nigerians in Sudan, such as recent travellers and long-established families who desire to return home.
Despite Mr Burhan’s invitation to the Jeddah summit, he is not expected to leave Sudan for security reasons, two other diplomats in the Gulf said.
But both sides have made it clear they would only discuss a humanitarian truce, not negotiate an end to the war.
Mr Buhari, accompanied by some of his aides, is expected to perform the lesser pilgrimage immediately after arriving in Mecca late Wednesday night.
