Al-Shabab has reportedly claimed responsibility for the bombings.
The Dadaab complex is the biggest refugee camp in the world, and Kenya wants it closed.
Al-Shabab is waging an insurgency against the Western-backed government in Somalia.
The Al-Qaeda-aligned group have launched regular attacks on African Union bases in Somalia.
Sagal Salad Osman worked for Radio Mogadishu.
Security forces say they still have not secured the hotel, which is popular with politicians.
At least 10 people killed after a suicide car bombing and gunfire at a popular hotel in the Somali capital.
Gunmen from the Al-Qaeda-aligned group killed 148 people in the April 2015 attack.
AMISOM is expected to play a key role in securing Somalia from Al-Shabab.
Al-Shabab says its fighters killed five soldiers in the clashes, a claim Nairobi denies.
U.S. and African Union forces reportedly participated in the offensive.
Kenya is currently hosting 600,000 refugees but wants to shut down their camps.
The Al-Qaeda affiliate looks set to disrupt elections scheduled for later in 2016.
ISIS claimed responsibility for an attack in Somalia for the first time in April.
Abdul Nadir Mumin defected from Al-Shabab to recruit fighters for ISIS in the failed state.
The Al-Qaeda aligned group is expected to increase attacks ahead Somali elections in 2016