Already more than 100 unidentified people have been buried who were burned beyond recognition.
The group has a history of not claiming attacks whose scale provokes massive public outrage.
Somalia's deadliest ever attack, a truck bomb in the capital Mogadishu, has now killed 358 people with 228 more injured, the government said late Friday, a major jump in the fatality toll.
A truck packed with explosives blew up in Hodan on October 14, destroying some 20 buildings in the bustling commercial district, leaving scores of victims burned beyond recognition.
Several experts told AFP the truck was probably carrying at least 500 kilos (1,100 pounds) of explosives.
"The latest number of casualties 642 (358 dead, 228 injured, 56 missing). 122 injured ppl flown to Turkey, Sudan & Kenya," Somali Minister of Information Abdirahman Osman tweeted.
Wounded
The figures mark a sharp increase in the toll, which earlier this week was put at 276 dead and 300 wounded.
The attack has overwhelmed Somalia's fragile health system, and allies from the US, Qatar, Turkey and Kenya have sent planeloads of medical supplies as well as doctors, with all except the US also evacuating some of the wounded.
Death tolls are notoriously difficult to establish in Mogadishu, with families often quickly taking victims away to be buried.
There has been no immediate claim of responsibility, but Al-Shabaab, a militant group aligned with Al-Qaeda, carries out regular suicide bombings in Mogadishu in its bid to overthrow Somalia's internationally-backed government.
The group has a history of not claiming attacks whose scale provokes massive public outrage.
Forensic tests
Already more than 100 unidentified people have been buried, who were burned beyond recognition.
While the rapid burial is partly due to Islamic culture, the Somali government also has no proper morgue nor the capability to carry out forensic tests to identify the victims.
Somali President Mohamed Abdullahi Mohamed vowed Wednesday to step up the war against Al-Shabaab, saying that the attack showed "that we have not done enough to stop Shabaab."
"If we don't respond to this now, the time will surely come when pieces of flesh from all of us are being picked up off the ground. We need to stand up together and fight Al-Shabaab who continue massacring our people," he said.
However it was unclear what Farmajo — who came into office eight months ago also vowing to eliminate Al-Shabaab — planned to do to stop the militants from carrying out such attacks.
The previous most deadly attack in Somalia killed 82 people and injured 120 in October 2011.
