At least 276 people have died and the government news agency Sonna says only 111 of them have been identified.
A Turkish military plane is taking 40 of the injured to Turkey for medical treatment.
It is the deadliest terror attack in Somalia since the Islamist al-Shabab group launched its insurgency in 2007.
Some of the bodies were burnt beyond recognition.
The country does not have a public health record database, and does not have the means to identify people using DNA.