One Shabaab fighter blew himself up in the car bomb late on Thursday, a huge blast that ripped the front off a major hotel and sparked a fireball blaze igniting several cars on the busy street.
Medics pulled five bodies from the wreckage immediately after the explosion, but the recovery of more bodies was blocked for hours by the ensuing fighting.
Other fighters from the Al-Qaeda-linked group stormed inside a building housing a restaurant, where they were ringed by police.
By Friday afternoon, they said the toll had climbed significantly.
"We have recovered 14 more dead bodies from under the rubble of collapsed buildings, bringing the total number of dead to 19," said Aamin Ambulance director Abdikadir Abdirahman, who added that at least 60 had been wounded.
"There are still some armed men inside a building," police officer Ibrahim Mohamed said on Friday, as sporadic bursts of gunfire and grenade explosions could be heard. "Security forces are trying to storm the building."
Shabaab insurgents said a suicide bomber from their group was responsible for the attack, in a bid to kill senior officials staying in the Maka Al-Mukarama hotel.