(Adds details, Chatham House report) By Sahal Abdulle MOGADISHU, April 25 (Reuters) - Shelling and machine-gun fire shook the Somali capital Mogadishu on Wednesday for an eighth day and residents fled a government offensive to crush Islamist insurgents and clan militia. Residents said Wednesday's fighting was lighter than in previous days. Allied Somali-Ethiopian forces are battling Islamist insurgents who have been frustrating the interim government's bid to restore central rule in the Horn of Africa nation for the first time in 16 years. "The shelling is still going on, but it is less heavy than yesterday. But it is still too dangerous to venture out," said one resident who asked not to be named. Locals, officials and human rights workers say nearly 300 people have been killed in a week of fighting that has focused on an Islamist stronghold in the north of the city. Somali media said leaders of the city's dominant Hawiye clan were holding more talks with Ethiopian army officers to try to find common ground for a ceasefire, but gave no other details. Hawiye elders could not immediately be reached for comment. For many Mogadishu residents, the fighting contrasts with the relative stability under the Islamists' six-month rule, before they were ousted in a war over the New Year. "This experience dramatically underlines the benefits of the brief period of 'Islamist' authority in southern Somalia which already begins to seem like a 'Golden Age'," Britain's Chatham House think tank said in a report on Wednesday. "The (government) is simply not trusted by the populace, nor does it represent the powerful interest groups in Mogadishu." The United Nations says more than 321,000 people have fled Mogadishu in recent weeks, many sleeping in the open or under trees. It has warned of a looming health disaster. BOMBINGS CLAIM As the battles intensified on Tuesday, a car bomb killed four civilians in central Mogadishu -- decapitating one -- and a suicide attacker struck at Ethiopian troops at a base in Afgooye, a small farming town on the western outskirts. An Islamist militant group claimed responsibility for both. The group, calling itself the Young Mujahideen Movement in Somalia, said a Kenyan member named Othman Otibo carried out the suicide bombing at the Ethiopian military base in Afgooye, 30 km (19 miles) west of Mogadishu. "Following this blessed martyrdom operation, a seven-minute clash broke out between the victorious lions of unification (Islam) and the remnants of the...defeated Ethiopians," it said in an Internet statement posted on Wednesday. The authenticity of the statement could not be verified. It was posted on a Web site used by Islamist militants fighting in Iraq, Afghanistan and Somalia. Ethiopian Prime Minister Meles Zenawi has said operations to defeat Islamist hardliners are going well, and that he expects it would take no more than "a week or two" to clear the city. (Additional reporting by Sami Aboudi in Dubai)