Somalis say the upsurge in violence is a result of regional commanders vying for position before the country's new government arrives.
Residents said on Monday the overnight clash in the city's northern Shibis neighbourhood erupted after armed men tried to extort protection payments in an area controlled by a rival militia.
"We have prepared our young boys to defend and secure our homeland zones of the Shibis district, so why should we pay this new money?" a Shibis elder, Ahmad Dhuhulow, asked.
Officials said one man's body was taken to a local hospital, while residents reported finding the bodies of two other armed men.
Somalia's new president, Abd Allah Yusuf Ahmad, has yet to return to Mogadishu after being elected in the security of neighbouring Kenya in October.
Residents said insecurity in parts of the capital had increased since then, as rival commanders fought to claim new territory before his administration is installed in Somalia.
Yusuf was sworn in on 14 October
Yusuf was elected on 10 October in the Kenyan capital Nairobi after almost two years of arduous peace talks hosted by Kenya because of security concerns in Somalia.
Somalia's own capital, the ruined, gun-ridden city of Mogadishu, was not considered safe enough for the ceremony.
Yusuf was elected by a 275-member interim parliament in a further step towards restoring government to the fractious, clan-based country that descended into anarchy in 1991 after the ousting of military ruler Muhammad Siad Barri.
A career soldier and leader of Somalia's autonomous Puntland state since 1998, Yusuf is tasked with establishing a government in Somalia, where heavily armed militias rule their areas by the bullet.