The summit statement also expressed "the complete support of the African Union and neighbouring countries for Sudan as it faces it political, security and economic challenges."
African leaders at an emergency summit in Cairo urged Sudan's military rulers on Tuesday to implement a democratic transition within three months, the Egyptian presidency said.
Egypt and representatives from several other African nations agreed on "the need for more time" for Sudanese authorities and political actors "to implement peaceful, organised and democratic transition measures," it said in a statement.
They also urged the African Union to extend by three months a deadline, currently the end of April, for Sudan's military council to hand power to a civilian authority or face suspension from the regional bloc.
That would partially ease international pressure on the council to hand over to civilian rule.
The army toppled longtime president Omar al-Bashir on April 11, but protestors have continued to hold mass rallies demanding a swift transition to a non-military government - calls the council has so far resisted.
However, it has said it was ready to accept a civilian government of technocrats to run the country during an interim period of up to two years that would prepare for a presidential election.
But protesters say the proposal would leave ultimate power in the hands of the military, demanding that the ruling council be staffed by civilians with military representation.
Heads of state and senior officials from states including Ethiopia, Nigeria, Rwanda and South Africa took part in the summit.
"We agreed today into the urgent restoration of a constitutional system through a democratic, political transition owned and led by the Sudanese themselves," said Egyptian President Abdel Fattah al-Sisi, who currently chairs the AU.
"This is to institute a comprehensively democratic political system and entrench the rule of law" as well as safeguarding human rights, he added.
The participating countries also said they would help Sudan tackle cross-border crime including arms and human trafficking in order to maintain "regional stability."