A suicide vehicle bomber first drove into a hotel where President Mohamed Abdullahi Farmajo was due to host a meeting on Saturday, following by a auto bombing near a former parliament building.
Following further explosions, police said they were battling militants on the top floor of the hotel, where more than 20 civilians may be trapped inside.
"Security forces have entered a small portion of the hotel building ... the exchange of gunfire is hellish", he said. One senior police official and a former MP were among the dead.
It noted its fighters were inside the hotel.
A huge cloud of smoke rose over the hotel and there were more than a dozen wrecked cars outside.
Bombs in Mogadishu two weeks ago killed at least 358 people, the worst such attacks in the country's history, igniting nationwide outrage.
The Nasa-Hablod hotel is frequented by government ministers, lawmakers and Somali business leaders.
Fellow witness Ismail Muktar said, "We can hear sporadic gunfire and grenade blasts and the area is very dark because the electric line was cut off amid the blast".
The Somali militant group Al Shabab said it carried out the bombings.
Al-Shabab, Africa's deadliest Islamic extremist group, quickly claimed responsibility for Saturday's attack and said its fighters were inside the hotel.
Following the blasts, witnesses reported hearing gunfire and said the entire area around the Nasa Hablod Hotel 2 had been sealed off by security forces to keep people away.
The US military has increased its strikes against al Shabaab this year with nearly 20 drone missions against the terror group.
Police Colonel Mohamed Abdullahi says the bomber stopped outside the heavily fortified hotel and pretended to fix the vehicle before finally turning it around and detonating. At least 358 people were killed and about 400 injured, with numerous victims burnt beyond recognition.
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