Somali troops and their Ethiopian allies pounded insurgent positions in the capital with bombs and tank shells Thursday, sending residents fleeing a surge in fighting that killed at least 10 people and wounded 50.

A witness reported seeing a dead soldier's body dragged through the streets.

The military operation was the beginning of a three-day push to restore order in Mogadishu as Ethiopian troops who helped oust an Islamic militia withdraw, said Mohamed Mohamud Husein, spokesman for the Somali president.

Despite near daily attacks from fighters believed to be the remnants of the Islamic militia, Ethiopia's prime minister said his forces had "broken the backbone" of the insurgents and that a majority of his troops had left Somalia.

At least six people — believed to be civilians — were killed in a gunbattle between Ethiopian troops and insurgents, residents said. One man, Bare Abdulle, said he saw a civilian dragging the body of an Ethiopian soldier and four other bodies lying in the street.

Bloodied civilians were seen running through the streets. Fifty wounded people were being treated at Mogadishu's Medina Hospital, said Sheikh Don Salad Ilmi, the hospital's director.

Leyla Ali Moalim said she and her children were separated when the fighting broke out.

"All my children took refuge in a mosque, where they are trapped," she told The Associated Press by telephone, her voice cracking. "They have not had their meals since this morning and I cannot go out of the house."

The Ethiopian troops met with stiff resistance from a dozen gunmen who used rocket propelled grenades, mortars and machine-guns, said Khalid Mohamed Arabey, who lives in southern Mogadishu. The Ethiopians responded with artillery and tank shells.

Helicopters dropped several bombs on insurgent positions.

"Two helicopters flew over us. One was making a surveillance and the other one was dropping several bombs," said Qoje Omar Gesey, a resident of the capital. He said the bombs fell near a former market in northern Mogadishu.

Ethiopian Prime Minister Meles Zenawi said his country had successfully accomplished its mission in Somalia. He said extremists were no longer a "clear and present danger" to Ethiopia, a predominantly Christian country that had feared the rise of a neighboring Islamic state.

"After breaking the backbones of extremist forces, our defense forces have started to withdraw," Meles told his country's parliament. He said more than two-thirds of his forces have returned to Ethiopia, but gave no figures.

Meles said his government would continue to train Somali security forces.

African Union peacekeepers who have been arriving to support Somalia's government have also come under attack. Last week, a cargo plane carrying equipment for AU troops was shot down by a missile during takeoff, killing all 11 Belarusian crew members.

Somalia has seen little more than anarchy for more than a decade. The government, with crucial support from Ethiopian troops, only months ago toppled the Council of Islamic Courts, the militia that had controlled Mogadishu.

The United States has accused the Islamic group of having ties to Al Qaeda.

The U.N.'s refugee agency said 57,000 people have fled violence in the Somali capital since the beginning of February, including more than 10,000 people who fled the city in the last week.

The figures were based on information provided by non-governmental organizations in Somalia, the U.N. High Commissioner for Refugees said.

"There has been a steady exodus from the city since the beginning of February, when armed groups clashed with forces of" the government, the agency said.

• Complete coverage is available in FOXNews.com's Africa Center.