Somalia's Union of Islamic Courts fighters have fled towards Kenya after abandoning their last stronghold on Monday in the southern town of Kismayo to government forces backed by Ethiopian troops, tanks and aircraft.
The Somalian government has asked Kenya to close its border to the group crossing into the east of the country.
Somalia's interim prime minister has offered an amnesty to the Islamic courts fighters.
Ethiopian backing has enabled the embattled government to break out of its provincial enclave and drive the militia from the capital, Mogadishu, and end their six-month control of much of the country.
Uganda has offered to send peacekeeping troops to Somalia within the next few days.
Mohamoud Hurreh, Somalia's foreign minister, told Al Jazeera on Monday that he expected the government to complete its victory over the Islamic courts.
"We are going to go after them until they surrender. We expect to finish them off."
For his part, Ali Jama, the Somali information minister, said the Islamic courts militia men and "foreign fighters" were headed towards Kenya and that the government had appealed to Kenya to seal its border.
Kenyan officials said they had not recieved orders to close the border but had reinforced ground and air patrols in the area.
On Monday, Ali Mohamed Gedi, the Somali interim prime minister, ordered all Somalis to hand over their weapons by Thursday.
He also offered an amnesty to Islamic courts fighters who surrendered their weapons, but said it did not extend to the group's leaders.
"If they fail to heed the orders of the government, the government will forcefully extract weapons from them," he said.
Gedi appealed to other world powers and aid agencies for "assistance to those people in the regions affected by the war and the flooding before that".
He also appealed for African Union forces to be stationed in the country.
Gedi said: "We are consulting with the African Union and the member states. They are still needed for their support in the pacification and stabilisation of the country. We would like the military observers and peacekeapers to come in to help us as soon as possible."
Final stronghold falls
Earlier on Monday, Islamic courts fighters fled from their final stronghold around the southern Somali port town of Kismayo in the face of an advancing force of Ethiopian and interim government soldiers.
|Ethiopia has about 4,000 troops in Somalia|
assisting transitional government forces [AP]
A Kismayo resident said: "The Islamic courts left Kismayo last night. They left [their front line at] Jilib as well.
"Nobody knows where they went. There's a lot of confusion."
The besieged Islamic courts had rallied several thousand fighters at Jilib, just north of Kismayo on the shores of the Indian Ocean, after a retreat south 300km from the capital, Mogadishu.
Ethiopian troops fighting to support the interim government had fired mortars and rockets at the UIC fighters dug in near Kismayo on Sunday to start a battle against them.
Fearing a bloodbath, residents ran for their lives, carrying blankets, food and water on their heads.
The Somali government said that despite its military successes it recognised that a political settlement was still vital in order to head off the possibility of an Islamist anti-government campaign.
The interior minister, Hussein Mohamed Farah Aideed, said: "If we do not reconcile with them, then they will start an insurgency like in Iraq."
The intervention of Ethiopia has reversed the fortunes of the provisional government and the Islamic courts, which two weeks ago controlled the capital and appeared on the verge of routing a weak interim government stranded in the provincial town of Baidoa.
Ethiopia says it has 4,000 troops in Somalia, though many believe that number could be far higher.