Initial reports say at least 10 people were killed in the first explosion and 6 others were injured.
Extremists attacked a Mogadishu hotel Saturday with a vehicle bomb, a suicide vest, grenades and firearms, killing at least 23 people, including a baby, wounding more than 30 and trapping dozens of people on the building's upper floors.
Police said earlier a suicide vehicle bomb had been rammed into a hotel and a former government building had been attacked.
Police officer Major Abdullahi Aden told Reuters the auto bomb said: 'They are fighting inside.
"Security forces have entered a small portion of the hotel building ... the exchange of gunfire is hellish", he said.
Speaking to the AP news agency by telephone, Captain Mohamed Hussein said that security forces were battling five extremists on the top floor of the hotel and that two of the attackers had been neutralized.
The attack comes two weeks after a truck bomb left 358 people dead in the city.
The al-Shabab militant group has claimed responsibility.
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"A auto loaded with explosives went off at the entrance of Nasa Hablod Hotel and there is gunfire", police official Ibrahim Mohamed told AFP, saying there was also "a minibus loaded with explosives which went off a nearby intersection".
Al Shabaab, which is affiliated with al Qaeda, has killed hundreds of Somalis as it seeks to impose its strict interpretation of Islamic law.
A local reporter told VOA he saw nine dead people.
Security forces cordoned off the area.
Somalia's government attributed that attack to al Shabaab. The hotel is close to the presidential palace.
U.S. military officials and others in recent months have expressed concern that Somali forces are not yet ready.
Al-Shabab, Africa's deadliest extremist group, claimed responsibility for the attack that killed a baby and two children, a senior Somali police colonel and a former lawmaker, Capt. Mohamed Hussein told the Associated Press.