Residents told the BBC the clashes began in the town centre at midday and lasted for about 40 minutes.
They broke out after one of the leaders tried to meet the defence minister who is attempting to resolve the crisis.
African Union troops are in charge of security in the city since capturing it from Islamist militants last October.
A new UN-backed government in Mogadishu is trying to regain control of the country after more than 20 years of conflict with the help of the AU force.
Assassination attempt
The BBC’s Mohamed Mwalimu in the capital, Mogadishu, says Kismayo is an extremely fertile area with a strategic port and has changed hands frequently over the last two decades.
There are about 20 different clans in the region – known as Jubaland – competing for control of Kismayo, about 480km (300 miles) south of Mogadishu.
At the moment, there are several self-declared presidents of Jubaland and the government has said it recognises none of them.
It wants the groups to come to a meeting in Mogadishu to resolve the issue – this is why Defence Minister Abdihakim Mahmoudis Haji is visiting the city.
Friday’s fighting started when fighters loyal to Ahmed Madobe stopped his rival Istin Hassan from meeting Mr Haji, who was staying at a hotel in central Kismayo.
Three civilians and four fighters died when the two sides exchanged fire, said residents and a medical source.
Both men have large militias and residents told the BBC they fear there may be more fighting as the two groups can be seen mobilising.
Mr Haji told the BBC Somali Service that such fighting “would not be tolerated and should stop forthwith”.
He denied allegations that members of the Somali army had joined the rival militias.
Losing Kismayo in October was a blow for al-Shabab, the al-Qaeda-linked Islamist group which controlled larges swathes of country in recent years.
The port – and especially the export of charcoal – provided the Islamists with important funding.
Although the AU and Somali government have driven al-Shabab from most major cities, its fighters still control smaller towns and rural areas in central and southern Somalia and they sometimes launch attacks in government-controlled territory.
On Friday, Mahad Abdirahman Adan, the security chief of the south-central Bay region, was ambushed by al-Shabab fighters on his way from the city of Baidoa to Mogadishu.
His driver was killed and Mr Adan is being treated in an AU hospital in Leego, about 60km north-west of Mogadishu.
The new government, formed last year, is the first one in more than two decades to be recognised by the US and the International Monetary Fund (IMF).