Ethiopia - where the continental bloc is based - planned a mediation effort, with Prime Minister Abiy Ahmed due on Friday to meet members of both the ruling Transitional Council (TMC) and the opposition, a diplomatic source said.
In handing down its suspension the Peace and Security Council, the AU's conflict-resolution body, said transferring power to a civilian-led authority was "the only way to allow the Sudan to exit the current crisis".
The African Union Peace and Security Council suspended Sudan from its activities Thursday after the death toll from a military crackdown on protesters climbed to more than 100.
Sudanese doctors allied with the opposition say 113 people were killed, and more than 500 others wounded in clashes.
"The Kingdom affirms the importance of resuming dialogue between the various parties in Sudan to fulfil the aspirations of the brotherly Sudanese people", the Saudi government said in a statement carried by the official SPA news agency.
A series of talks between the military and protesters has broken down, decreasing the likelihood of a swift transition deal. The government has put the week's death toll at 61, including three members of the security services.
The deputy head of the military council defended the violent suppression, claiming that the protesters had been infiltrated by rogue elements and drug dealers.
The Transitional Military Council welcomed Abiy's statement and said that it is open to negotiations and ready to come to an agreement at any time.
On Wednesday it was revealed that hundreds of bodies were pulled from the River Nile in Khartoum as a result of the crackdown. The violent June 3 attack aimed to disband the protesters who had been camped out since the days before former President Omar al-Bashir's ouster on April 11.
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The attack caused an global outcry, drawing strong criticism from the United Nations, European Union, African Union and other observers.
"They were taken with vehicles that belong to the Janjawid militias to an unknown destination", The Central Committee of Sudan Doctors (CCSD) said in a statement on Facebook.
While African and Western governments have been strongly supportive of the protesters, Riyadh and its allies, which are deeply hostile to popular movements in the region, have provided the military council with desperately needed aid. Witnesses said traffic was flowing again on main roads, although many shops remained closed.
Washington on Wednesday called on Sudan's military rulers to "desist from violence" and urged talks with protesters to resume.
In the early morning, sporadic shooting was heard in the Khartoum 2 neighbourhood, an area where there are several embassies.
General Abdel Fattah al-Burhan, the military ruler, has offered to hold elections in nine months, upturning an earlier plan of a two-year transition.
"We will continue in our protests, resistance, strike and total civil disobedience", he said.
"This call is not serious", association spokesman Mohammed Yousef al-Mustafa told The Associated Press.
The suspension deprives Sudan's ruling military council of worldwide legitimacy, according to Amani Africa, an independent think tank based in the Ethiopian capital, Addis Ababa.