"We understand it is a suicide car bomb near the presidential palace area. Then another blast followed, with gunfire. It is too early to know details and target," Major Mohamed Ahmed, a police officer said.
The director of Aamin Ambulance service, Abdirahman Abdulqadir, said that 18 people were killed and another 20 were injured people after the blasts.
The Twitter users have uploaded videos and pictures allegedly showing the plumes of thick smoke rising in the sky after the explosions.
The blasts have reportedly caused damages to the nearby houses.
This is the latest terrorist attack in Mogadishu in the past few months. In January, a car bomb explosion wounded two people and a roadside landmine blast claimed lives of five Somalian troops.
Somalia has in turmoil for decades after the eruption of a civil war between in the early 1990s. The Al-Shabaab group, that had sworn allegiance to the al-Qaeda terror group, is staging numerous attacks across Somalia with an ultimate goal of imposing a radical version of Sharia law in the country.