Salad Ali Jelle, Somalia's deputy defence minister, said the joint government and Ethiopian forces on the ground outnumbered the Islamic courts fighters in Jilib by more than two to one.
"The Islamists are very weak now," he said.
Islamic courts leaders had regrouped their forces in Jilib and Kismayo after abandoning the capital, Mogadishu, on Thursday in the face of Ethiopian firepower.
Hussein Aidid, deputy prime minister in the transitional government, urged Islamic courts leaders to surrender, disarm and avoid more of the fighting that has killed hundreds, and possibly thousands.
The transitional authority is recognised as Somalia's legitimate government by the UN and the African Union.
"The Somali UIC made miracles to bring peace and stability but the world is choosing to go for the so-called government just because of Islamophobia"
Xaqudirir, Mogadishu, Somalia
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Aidid said: "We will surround them but we will leave open [an opportunity] for dialogue and negotiations for them to disarm."
So far, the offer of peace talks has fallen on deaf ears, with the Islamic courts leaders refusing to discuss surrender.
Sheikh Sharif Sheikh Ahmed, the group's leader, told residents in Kismayo on Saturday: "I want to tell you that the Islamic courts are still alive and ready to fight against the enemy of Allah.
"We left Mogadishu in order to prevent bloodshed in the capital, but that does not mean we lost the holy war against our enemy."
Ahmed told Al Jazeera on Sunday: "We decided to fight the enemy in every area."
On Sunday, as Somali transitional government and Ethiopian forces, riding in 16 Ethiopian tanks and accompanied by armoured vehicles and artillery, swept southwards, they were met by as many as 2,000 civilians fleeing the expected fighting.
"The Islamic militia told us they are committed to defend the town to the death, so we have no other option but to flee," Ilse Ali Ilweyn, a father of six who lives in Jilib, said.
Osman Mohamed, an aid worker in the area, said: "Two thirds of the population in Jilib have fled the town ... nearly 4,700 have fled."