Clashes between Somali government troops and al-Shabab fighters have left 15 people dead and at least 45 civilians injured, medics and witnesses say, Press TV reported.
Al-Shabab fighters, with the aim of toppling the weak president backed by African Union troops, have launched a new offensive to take Mogadishu.
Fighting began on Sunday night, stopped overnight, but resumed on Monday morning on various fronts of the northern districts of Abdiasis, Shibis, Karan, Daynile, and Bondhere.
Several mortar shells and heavy gunfire also rocked the northern district of Hamar Weyne, where al-Shabab fighters tried to advance.
After exchanging artillery and gunfire for hours, late on Monday both sides claimed victory but denied causing civilian deaths and injuries, AllAfrica news quoted Somalia's Radio Garowe as reporting.
Al-Shabab has claimed that its fighters have captured several areas.
However, Somali government officials have rejected the al-Shabab claims, saying their troops are still in control of the contested areas.
The two sides have been battling for the same districts for months without gaining much ground.
Over 21,000 people have been killed in the fighting in Mogadishu since early 2007.