Somali government forces are advancing on Kismayo, the key stronghold of Islamist group al-Shabab, as thousands of residents flee an expected assault.
A Somali government army general told the BBC that his forces were intending to take the port, but did not say when.
The United Nations refugee agency has reported a sudden spike in the number of civilians fleeing Kismayo from a few dozen to more than 1,000 a day.
Those who can afford it are hiring buses and trucks to leave the city.
Kismayo is the militants' main base in its fight against the Somali government whose troops have been slowly converging on the town with African Union (AU) soldiers - de-mining the road along the way.
The UN says residents there fear some sort of military activity in or around the port.
Locals told the BBC Somali Service that hundreds of militants have also been leaving Kismayo in armed pick-up trucks, taking heavy equipment with them. Radio Andalus, the mouthpiece of al-Shabab in the city, has reportedly stopped broadcasting.
But al-Shabab denies the reports, saying they have fought off AU forces.
Appeal for calm
Somali army Gen Ismail Sahareed, who said he was speaking from a position about 60km (37 miles) outside Kismayo, told the BBC Somali Service that al-Shabab had left the port and that his troops were on the way there.
"In the last battles [on Saturday and Monday] we defeated al-Shabab's defence forces and they ran away and we are chasing their remnants."
The general said the governor of Kismayo had been wounded in the fighting.
He appealed for Kismayo residents to be calm and promised the Somali government army would bring all areas in the region under government control in the near future.
He warned that al-Shabab had left behind guns, distributed amongst the population to create insecurity once government troops arrive there. He appealed to residents not to use them, saying that his troops would collect them.
However, Muhammad Usman Arus, a spokesman for the al-Qaeda-affiliated group, told the BBC that al-Shabab had killed around 100 Kenyan and Somali troops and pushed them back from Kismayo.
"We are in Kismayo - this is a propaganda war. The Kenyan and Somali forces have already broken off and gone back to their positions," he said.
Analysts say that losing their strategic stronghold would be a major blow to al-Shabab. Located in the south of Somalia, near the border with Kenya, the port exports charcoal generating millions of dollars to fund the militants' fight against the government.
BBC international development correspondent Mark Doyle says if Somali government forces do move on Kismayo it will be largely thanks to their allies in the AU force - the Kenyans operating around Kismayo and Ugandan troops operating to the north of the city.
The United States supports the AU forces officially with logistics but also sometimes also with drone strikes.
A navy spokesman in Washington confirmed there is a US warship off the coast of Kismayo but said it was on routine operations.
The spokesman said he had no information about whether the ship intended to dock in Kismayo or not.