Nairobi, Kenya (CNN) -- Thousands of civilians are fleeing one of the final strongholds of an al Qaeda-linked militant group in Somalia, according to the U.N. refugee agency.
"So far this month, more than 10,000 people have fled from Kismayo fearing the resumption of fighting. Movements substantially increased on Monday and have been continuing since. Some 7,500 people fled the area in the past four days amid growing tension," UNHCR spokesman Adrian Edwards said in a news conference in Geneva.
The agency said that Somalis were leaving in minibuses, in trucks and on donkey carts.
Kismayo, a port city south of the capital of Mogadishu, is a key potential battleground between African Union forces and Al-Shabaab, a group that has long tried to overthrow the Somali government but has been increasingly beleaguered.
The exodus of civilians comes as AMISOM, the African Union force, announced that it had captured Janaa Cabdalla, a town about 25 miles (40 kilometers) from the center of Kismayo.
A spokesman for the Kenyan Defense Force, which makes up the majority of troops in the offensive, said they were using land, sea and air forces to attack Al-Shabaab and degrade its forces before an eventual attack on Kismayo.
"We need to consolidate or position first before we attack," Col. Cyrus Oguna said.
Oguna said that Al-Shabaab militants have been leaving Kismayo in pickup trucks in recent days, leading to speculation that some were fleeing before a major offensive. "We don't know if they are fleeing or just regrouping to mount an insurgency against our troops," he said.
Al-Shabaab has denied that anyone has left. "It is blatant lies," the group said on its Twitter feed.
Military analysts believe, however, that Al-Shabaab is militarily cornered. After losing control of much of Mogadishu last year, Kismayo became even more critical to the militant group. Al-Shabaab uses the port to garner much needed tax revenue from the illegal charcoal trade and smuggling operations.
Since crossing into Somalia in October, Kenyan commanders and politicians have stated more than once that capturing Kismayo was the ultimate aim of their operation, saying several times that an attack would be "imminent."
Bad weather, operational difficulties and costs, and a cautious approach have all played into the more deliberate nature of the campaign.
Aid officials worry that the push into Kismayo could have a severe impact on civilians.
In an apparent attempt to ease those fears, the African Union put out a statement this week saying it was committed to "minimizing the impact of its operations."
"AMISOM takes responsibility for the safety of the people of Somalia very seriously and fully understands its obligations to conduct operations without causing undue risk to the local population," said Boubacar Gaoussou Diarra, an African Union special representative.