Many internally displaced families in the Faanole neighbourhood of the city abandoned their camps as fighting broke out on Monday. Some set up temporary shelters away from the area and others headed towards the Kenyan border. At least 25 people reportedly died in the town.
Kismayo is 500km south of the capital, Mogadishu. A local journalist, who declined to be named, said the Majeerteen militia - of President Abdullahi Yusuf's Darod sub-clan - had been pushed out of the city by the Marehan - also of the Darod sub-clan, to which the Defence Minister Barre Hiirale belongs - and was now camped outside the city.
However, Ahmed Abdi Umar, the deputy governor of Lower Juba - of which Kismayo is the regional capital - downplayed the displacement. Many people, he added, were already returning home, adding that no displaced people had gone towards the Kenyan border. "They moved to other areas within the city for safety," he said.
According to other sources, tension had been building between the two groups over power-sharing within the administration. "It just boiled over yesterday [Monday]," said a business source. The two groups, he added, had been forced to merge into one army unit, but later disintegrated into clan militias.
Muhammad Ahmed, a local journalist, said Kismayo was still tense. Many businesses had not opened for business on Tuesday.
Meanwhile, Mogadishu entered the sixth day of fighting between Ethiopian-backed government troops and insurgents on Tuesday.
The fighting occurred mostly in the north of the city, according to a local source. He said shelling by Ethiopian and government forces on the north Mogadishu neighbourhoods of Jamhuriya and Towfiiq, insurgent strongholds, was continuing.
The insurgents comprise the remnants of the Union of Islamic Courts and Hawiye (the dominant clan in the city) militias, who are opposed to the transitional government and the presence of Ethiopian forces.
Meanwhile, the United Nations Secretary-General Ban Ki-moon on Monday called for an end to the violence in Somalia.
"The Secretary-General is gravely concerned about the continuing heavy fighting in Mogadishu, which has reportedly killed more than 250 people and forced more than 320,000 from their homes in the past six days alone," spokeswoman Michèle Montas told reporters in New York.
Ban called on the parties to "immediately cease all hostilities and to facilitate access for the delivery of urgently needed humanitarian assistance", renewing his call for an urgent resumption of political dialogue.
Separately, the Norwegian Refugee Council (NRC) urged the UN Security Council and the international community to work for an immediate cessation of hostilities in Mogadishu to secure humanitarian access to displaced populations.
"All parties to the conflict and the international community must work to initiate an all-inclusive peace process to avoid clan warfare in south-central Somalia," NRC's International Director, Jens Mjaugedal said ahead of a Council meeting on Somalia due on Tuesday.