The wounded included three ICRC staff members, the Red Cross added in a statement.
"The humanitarian convoy, consisting of three ICRC vehicles and three buses, all clearly marked with the Red Cross emblem, was due to evacuate over a hundred vulnerable civilians from Khartoum to Wad Madani when it came under attack upon entering the evacuation area," the statement read.
Sudan's civil war broke out in April, and since then has displaced 4.2 million people. (AP PHOTO)
The ICRC said it is shocked and appalled by the attack, which it described as deliberate.
It did not point the finger at any party, but Sudan's army said the convoy had come under fire after violating an agreement by approaching its defensive positions, using a car "belonging to the rebels" - a reference to the paramilitary Rapid Support Forces (RSF).
The ICRC convoy was evacuating civilians, including foreign nationals, from St. Mary's Church in Khartoum, according to the army.
In a separate statement, the RSF accused the army of attacking the convoy. It said the incident had resulted in deaths as well as injuries.
"The humanitarian operation had been requested by and coordinated with the parties to the conflict, who gave their agreement and provided the necessary security guarantees," the ICRC said.
The army and the RSF have been locked since mid-April in a conflict that has devastated Khartoum and triggered waves of ethnic killings in Darfur despite several diplomatic efforts to halt the fighting.
A power struggle erupted in April between the Sudanese army and the RSF paramilitaries. (EPA PHOTO)
Earlier, an African regional body involved in efforts to mediate over the war in Sudan said it had secured a commitment from warring parties to implement a ceasefire and to hold a political dialogue aimed at resolving the conflict.
There was no immediate comment from Sudan's army or the paramilitary Rapid Support Forces (RSF), which have been locked since mid-April in a conflict that has devastated the capital Khartoum and triggered waves of ethnic killings in Darfur despite several diplomatic efforts to halt the fighting.
At talks on Saturday in Djibouti, the current chair of the Intergovernmental Authority on Development (IGAD), Sudan's army chief Abdel Fattah al Burhan, agreed to a one-on-one meeting with RSF commander Mohamed Hamdan Dagalo, an IGAD statement said.
In a phone call Dagalo, widely known as Hemedti, also agreed to the ceasefire proposal and a meeting with Burhan, the statement said.
Burhan and Hemedti had "accepted the principle of meeting within 15 days in order to pave the way for a series of confidence-building measures between the two parties that lead to the launch of a political process", said Alexis Mohammed, adviser to Djibouti's president.
Earlier, in an address the Djibouti meeting, Burhan accused the RSF of "barbaric attacks" but said the army had not closed the door on finding a peaceful solution.
Hemedti, whose whereabouts are unknown, addressed the IGAD meeting remotely, blaming the outbreak of the war on loyalists of former president Omar al-Bashir who are powerful within the army. He called for reform of the army and the formation of a civilian government.
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