Heavy fighting has broken out between Somali government forces and al-Shabab rebels in the capital of Mogadishu, as Kenyan forces continue to advance across southern Somalia in an effort to hunt down members of the Somali insurgent group.

Officials and witnesses said African Union-backed Somali forces launched an assault Thursday in Mogadishu's Daynile district, one of the few remaining pockets of the Somali capital still controlled by the al-Qaida-linked militants. Somali officials say they are now in control of most parts of the district.

Al-Shabab abandoned most of the city in August, but has continued to carry out guerilla-style attacks against Somali citizens and government forces.

Meanwhile, Kenyan troops continue to advance across southern Somalia in an effort to clear the area of al-Shabab fighters. Kenya blames the Islamist group for the kidnapping of several foreigners in Kenyan territory — an allegation al-Shabab denies.

On Thursday, Kenyan President Mwai Kibaki said his country would use “all measures necessary” to ensure Kenyan peace and stability, saying the military operation was meant to protect Kenyan sovereignty.

The Kenyan army said Wednesday that it has killed at least 73 militants since launching the incursion a few days ago.

Kenyan forces are reported to be in the Gedo and Lower Jubba regions of southern Somalia.

Meanwhile, a Kenyan security minister says the government will conduct a sweep to catch suspected al-Shabab and al-Qaida sympathizers in Nairobi.

Speaking to parliament Wednesday, Internal Security Assistant Minister Orwa Ojodeah said al-Shabab is like a big animal with its tail in Somalia and its head in Kenya. He promised a massive operation against the group's supporters.