Auditor general Nur Farah's bodyguards opened fire on a vehicle carrying Abbas Abdullahi Sheikh Siraji, the public works and reconstruction minister, near a checkpoint close to the palace, said police captain Mohamed Hussein. Another minister who was in the auto with Siraji survived.
The 31-year-old Abbas Abdullahi Sheik Siraji was appointed Minister of Public Works and Reconstruction by Prime Minister, Hassan Ali Kheyre in March this year.
Police in Somalia say three soldiers have been arrested in connection with the killing of a government minister near the presidential palace.
"We are deeply saddened by the devastating news of the death of minister Abbas Siraji and we are passionately grieving with his family as they pass through this hard time", Khaire said.
The president-known as Farmajo-had given the militants 60 days to surrender, but the militant group dismissed the declaration as a statement made "just to please the West", the BBC reported.
The slain minister was driving his vehicle when the government soldiers opened fire and killed him in the process.
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Mohamed said he had ordered an investigation into what he termed "this unfortunate tragedy".
Militants from the al Qaeda-affiliated group al Shabaab have carried out frequent attacks in Mogadishu as they fight to topple Somalia's Western-backed government and drive out African Union peacekeeping troops.
The late minister had been the youngest in Somalia's new Cabinet.
The deceased lawmaker was a former refugee who grew up in Dadaab camp in Kenya, home to hundreds of thousands of Somalis who fled drought and civil war.
His story was widely seen as an inspiration for a country which has suffered conflict and anarchy for the last 25 years.