A suicide bomber drove the vehicle which was loaded with explosives towards a security checkpoint in the town of Beledweyne on Saturday, triggering an explosion that left scores trapped under bricks and concrete.
The death toll from the bombing attack has reached 21, according to an AP report citing local authorities on Sunday. However, a deputy police chief told AFP that the toll had climbed past the 13 deaths reported earlier but could not provide an exact figure.
"The search and clearing operation is going on at the site of the explosion and dead bodies were recovered this morning under the debris of some buildings," said Sayid Ali, deputy commander of the Beledweyne police station.
"There are concerns the death toll may increase further," he said, adding that the bomber had targeted a busy neighbourhood that housed businesses and residential buildings.
Somalia's President Hassan Sheikh Mohamud condoled the attack, doubling down on his vow to "eliminate" Al-Shabaab militants who have waged an insurgency against the country's fragile central government for over 15 years.
"Incidents like this will never deter us from continuing to eliminate the... terrorists," he said.
There was no immediate claim of responsibility for Saturday's bombing, which came after Somalia's beleaguered government admitted to suffering "several significant setbacks" in its fight against the Al-Qaeda-linked militants.
Ahmed Yare Adan, a local police officer, told AFP on Saturday that the attack had killed 13 people and wounded 45.
Somali Deputy Health Minister Mohamed Hassan said late Saturday that "around 13 seriously wounded people (were) evacuated from Beledweyne tonight" and brought to the capital Mogadishu for treatment.
Mohamud took office in May last year vowing "all-out war" against Al-Shabaab, who were driven from Mogadishu in 2011 but still control swathes of the countryside.
An African Union force deployed in Somalia in 2007 with a six-month mandate but still remains on the ground.
UN resolutions call for the African Union Transition in Somalia (ATMIS) force to be reduced to zero by the end of next year, handing over security to the Somali army and police.
But this has proved challenging, with the government now seeking to delay a planned reduction of ATMIS troops.
Somalia launched a major offensive against Al-Shabaab in August last year, joining forces with local clan militias in an operation backed by ATMIS troops and US air strikes.
But Somalia's national security adviser recently wrote to the United Nations requesting a 90-day delay to the planned pullout of 3,000 ATMIS troops by the end of September.
In the letter, seen by AFP, he said the government had "managed to re-liberate towns, villages and critical supply routes" during its offensive but had suffered "several significant setbacks" since late August.