African Union (AU) Commission Chairman Alpha Omar Konare told reporters on Thursday, "We have called for a halt to the bombings... We received promises today from Khartoum."
Sudan is also agreeable to the AU's deployment of an armed force to protect the pan-African body's ceasefire observers in Darfur, where 15 months of conflict have spawned what the UN has called the world's worst humanitarian catastrophe.
Konare, speaking at the close of the annual AU summit in Addis Ababa, said he hoped this force would be sent by the end of July.
The AU aims to deploy 300 armed troops. Asked when the force would arrive in Darfur, Konare said, "I hope before the end of the month because time is running out."
About 25 AU observers are on the ground in Darfur.
At least 10,000 people have been killed in Darfur, mostly by a feared militia allied to Khartoum. Another 1.2 million have been displaced, with more than 100,000 of them seeking refuge across the border in Chad.