The helicopter was downed after Ethiopian troops supporting the interim Somali government launched air attacks on armed groups for the first time since the start of the year.
Ethiopia said on Friday its military has killed 200 armed opponents during a major offensive in the capital.
"Ethiopia has killed 200 armed remnants of the Islamic Courts Union and wounded many others," Ethiopia's information ministry said in a statement broadcast on national television.
"I think Ethiopia's role in Somalia now has to be fair and unbiased"
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One resident, Qoje Omar Gesey, said of Thursday's aerial assault: "Two helicopters flew over us. One was making a surveillance and the other one was dropping several bombs."
He said the bombs fell near a former market in the northern part of the capital.
Earlier on Friday morning, a mortar shell struck a residential area in the south of Mogadishu, the capital, residents said.
Faisal Jamah, a resident who witnessed the attack, said: "There are a lot of wounded, but there is no way to take them to the hospitals due to the fighting on the roads."
Ban Ki-Moon, the UN secretary-general, has expressed concern over the use of helicopters to attack positions inside the city.
Ban is "particularly concerned about the use of air strikes and the introduction of tanks and heavy artillery into densely populated parts of the city, further increasing the security threat to large numbers of civilians," Farhan Haq, a UN associate spokesman, said in New York.
Ban called for an immediate halt to the fighting.
"The secretary general emphasises once again that sustainable peace in Somalia can only be attained through an inclusive dialogue leading to a political solution and national reconciliation," Haq said.
Gunfire has also been reported near the presidential palace.
The ICRC said on Friday that it deplored the heavy civilian toll, in what it said was the worst fighting in Mogadishu for 15 years.
More than 200 people, mostly civilians, had been admitted to the city's main Keysaney and Medina hospitals in the 24 hours since Thursday morning, the ICRC said in a statement.
"The population of Mogadishu is caught up in the worst fighting in more than 15 years. The ICRC deplores the high number of civilian casualties," the Geneva-based humanitarian agency said in its statement.
"It urgently calls on all parties to respect the rules of international humanitarian law and take all feasible precautions to spare civilians and their property," it said.
Dragged through the streets
Seven Ethiopian soldiers were said to have been killed on Thursday, with witnesses in the southern district of Shirkole reporting the bodies of Ethiopian troops were dragged through the streets.
Loudspeakers transmitted calls for residents to come out and fight the Ethiopian troops.
The scenes echoed violence last week, when crowds burned the bodies of two dead Somali soldiers.
|More than 10,000 people have fled |
fighting in the city in the past week [AFP]
The fighting on Thursday brought an end to a ceasefire agreement in place since the weekend.
But Mohamed Mohamud Husein, a spokesman for the Somali president, said the fighting marked the beginning of a three-day push to restore order in Mogadishu, as Ethiopian troops, who helped the Somali government oust Islamic Courts fighters last year, withdraw from the capital.
In Ethiopia, Meles Zenawi, Ethiopia's prime minister, said that more than two-thirds of his forces had returned home, but gave no figures.
In a speech to his country's parliament, he said "extremists" in Somalia were no longer a "clear and present danger" to Ethiopia.
"After breaking the backbone of extremist forces, our defence forces have started to withdraw," Zenawi said, adding that his government would continue to train Somali security forces.
But continued heavy fighting in Mogadishu is causing many residents to flee.
The UN's refugee agency estimates 57,000 people have fled the Somali capital since the beginning of February, including more than 10,000 people who left in the past week.