Ethiopian helicopter gunships have fired at a market near an insurgent stronghold in the Somali capital.
Many civilians had been injured and wounded in recent weeks
The BBC's Mohammed Olad Hassan in Mogadishu says hundreds of insurgents armed with rocket launchers and machine guns are battling Ethiopian troops.
Ethiopian tanks are also deployed. Crowds dragged several dead bodies in uniform through the streets.
The security crackdown in the south of the city is being billed as a three-day operation to restore order.
Meanwhile, Ethiopia says two-thirds of its troops have withdrawn from Somalia.
Ethiopian Prime Minister Meles Zenawi told parliament the rest of his troops, which are deployed in support of the interim government, would leave in consultation with the African Union.
Ethiopian troops helped install the government last December but have been gradually handing over responsibilities to the AU force that was deployed to Mogadishu this month to try and bring stability to the city.
Some 1,700 Ugandan troops are in Mogadishu as the advance party of a planned 8,000 strong AU force.
In a dawn operation, at least six people died in the fighting which broke a ceasefire declared a week ago and was brokered by elders form the Hawiye clan - the biggest in Mogadishu - but Ethiopia denied reaching any deal.
Ethiopian tanks, troops and helicopters are trying to take control of five key junctions.
The militia responded with heavy artillery fire.
The southern part of Mogadishu, where the fighting is going on, has become a no-go zone.
Dozens of injured civilians are stranded, as heavy fighting has grounded public transport and other business activity in the Somali capital.
"This is the worst fighting Mogadishu has seen since the Islamists were ousted. Explosions can be heard all over the city and many people are just holed up in their homes," resident Zenaib Abubakar told the BBC Somali Service.
Ms Abubakar said heavy shelling is taking place near the main stadium, where Ethiopian and government troops are battling with insurgents who are putting up heavy resistance.
"It's difficult to tell how many people have been injured or killed because fighting is taking place in several parts of the capital and communication today is not very good," said another resident, Ahmed Noor.
The interim government has blamed the escalating violence in the capital on remnants of the Union of Islamic Courts (UIC).
Somalia enjoyed a six months lull in the insecurity that had dogged the country in the past 16 years, when the UIC took power last year.
But insecurity has returned to the city.
The UN estimates that 40,000 people have fled Mogadishu since February.