Colonel Cyrus Oguna said the attack was part of a push by an African Union (AU) force to capture the city.
Residents told the BBC that al-Shabab was reinforcing its positions in the city and people had started to flee.
AU forces have vowed to capture Kismayo - a port city that is key to financing and arming the al-Qaeda affiliate.
The move on Kismayo comes as Somali MPs prepare to choose a new president under a UN-brokered peace plan.
The election is due on 10 September.
'Lucrative charcoal trade'
Kismayo residents said the port area was shelled twice and the airport three times.
Al-Shabab was testing its weapons and mounting guns on battle wagons, the residents said.
Some residents were fleeing, either towards the capital, Mogadishu, or the border with Kenya, amidst fears that a big battle could take place, they added.
Last month, al-Shabab lost control of Merca, the third biggest port city after Mogadishu and Kismayo, to AU and pro-Somali government forces.
In June, Kenyan Prime Minister Raila Odinga appealed to the US and EU to give financial aid for a "final onslaught" on Kismayo.