Defeated Somali Islamists fled their defences near a southern town and headed towards the Kenyan border on Monday (January 1) in what looked like the end of a nearly two-week war with the Ethiopian-backed government. Prime Minister Mohammed Ali Gedi speaking in Mogadishu, said several thousand Islamist fighters, who abandoned the capital to take a stand 300 km (186 miles) to the south near the port of Kismayu, melted away again overnight after trading artillery fire with advancing Ethiopian and government troops. The leaders and fighters of the Somalia Islamic Courts Council (SICC), driven from Mogadishu on Thursday after occupying it for six months, headed further south along the Indian Ocean coast towards neighbouring Kenya, residents said. They have vowed to hit back with guerrilla tactics. Some Kismayu residents said the Islamists were going to the hilly region of Buur Gaabo, just on the Somali side of the border. In its newly captured capital Mogadishu, the triumphant Somali government renewed its appeal for people to surrender their weapons to the government to help stabilise the Horn of Africa nation, in chaos and without central rule since 1991. "Those who have been misled by international terrorist themselves, those who flew away from the capital city purposely or following the misleading of the terrorists are called upon to come back....(pause). The government is providing amnesty for them," Prime Minister Ali Mohamed Gedi told journalists in Mogadishu. Gedi said Mogadishu residents would have three days from Tuesday (January 2) to hand over weapons in one of the world's most dangerous and gun-infested cities -- or be disarmed by force. The government also urged Kenya to close its north-east border and arrest any Islamists who made it across. But the long and porous border is tough to patrol, with ethnic Somalis populating the Kenyan side and nomads crossing easily. Diplomats said U.S. boats were believed to be patrolling the sea off Somalia to prevent SICC leaders, or foreign militant supporters, from escaping. Some Islamist fighters may simply have dumped their uniforms and melted into the Somali bush. The retreat of the Islamists caps a remarkable advance by the joint Ethiopian and government force. Just two weeks ago, the Islamists had appeared on the verge of routing the government, which had no control beyond its base in the provincial town of Baidoa. However, the intervention of Ethiopia -- the Horn of Africa's military power whose move into Somalia had tacit U.S. support, according to diplomats -- reversed that. Air strikes and heavy artillery bombardments quickly routed the Islamists. Witnesses at Jilib, north of Kismayu, said mortar and rocket fire between the two sides stopped eerily late on Sunday. "As everybody is following, there was fighting in Jilib area last evening when the defeated Islamic courts and the international terrorists together re-organised themselves and started attacking the government forces in that area, again they have been defeated very easily and the forces are still they chasing them," Prime Minister Ali Mohamed Gedi added. The joint Ethiopian-government force was marching into Kismayu early on Monday, its columns slowed by having to clear mines left by Islamists on the road in. Some residents took advantage of the temporary power vacuum to loot the Islamists' arsenal in Kismayu. While Ethiopian Prime Minister Meles Zenawi and President Abdullahi Yusuf and Prime Minister Gedi of the Somali government will be delighted with the Islamists' flight, political analysts say the conflict may be far from over. The Islamists, who had swollen their ranks with foreign Muslim fighters, may now concentrate on Iraqi-style insurgency tactics against a government they see as illegitimate and propped up by a hated and Christian foreign power. Islamist fighters were believed to number about 3,000. Ethiopia says it has 4,000 troops in Somalia, although many believe the figure could be far higher. Born out of sharia courts operating in Mogadishu, the Islamists threw U.S.-backed warlords out of the capital in June. They brought order to Mogadishu for the first time since 1991 when warlords ousted a dictator. However, some of their hardline practices -- such as closing cinemas and holding public executions -- angered Somalis, traditionally moderate Muslims. Both Addis Ababa and Washington say the SICC is a dangerous Taliban-like movement linked to al Qaeda, an accusation the movement says was trumped up to justify foreign intervention. Government leaders Yusuf and Gedi face a monumental task to tame a nation U.S. forces left more than a decade ago after an ill-fated intervention.