Recent fighting alone has displaced more than 60,000 civilians
The "very dire" humanitarian crisis in Somalia is the worst in Africa for many years, says Oxfam's co-ordinator for the failed Horn of Africa state.
Many of its hundreds of thousands of internally-displaced people, the world's largest such concentration, have little food or shelter, he said.
Mogadishu civilians have been fleeing intense fighting between Islamist guerrillas and pro-government forces.
The government says it has regained control of a second part of the city.
Mogadishu's deputy mayor Abdifitah Ibrahim Shawey said Islamist insurgents had been ousted from Dharikinley police station in the south-west of the capital, after the government took Yaqshid police base in the north of the city on Monday.
Following an upsurge in violence over the past month, some 200 people are crossing the border into Kenya each day, the UN says.
Aden Mohamed Nur, 80, had managed to stay in Mogadishu throughout the last 18 years of conflict, but has just arrived in Kenya after a week-long journey.
"My son was kidnapped. After five days he was released by his captors. That's the time I decided to flee for the Kenyan refugee camps," he told the BBC.
"I left behind all my property."
The BBC's Mohamed Olad Hassan in Mogadishu says city-dwellers are taking advantage of a relative lull in the fighting on Tuesday to get out, carrying light belongings in the arms.
Many thousands of people, mainly women and children, have fled to Afgooye, just south of the city where most are sheltering under trees with little to eat or drink, he says.
Hassan Noor, Oxfam's humanitarian co-ordinator for Somalia, told the BBC's Network Africa programme circumstances in the capital were "very dire".
"The situation is really appalling," he said.
"There are hundreds of children all over the area with tubes on their faces and [saline] drips on their hands. Some of them are actually unconscious and suffering from all sorts of diseases, mainly acute diarrhoea and cholera."
"I have seen the situation in Darfur, northern Uganda, some parts of Congo, but what is actually happening now in Somalia is indeed the worst kind of humanitarian situation in Africa in many years," he added.
Radical Islamist militia groups, Hisbul-Islam and al-Shabab, have been locked in see-sawing battles in the Somali capital with pro-government forces that have displaced more than 60,000 civilians since 7 May.
Pro-government forces have been pressing on with a counter-offensive launched last week against the insurgents, who control swathes of southern and central Somalia.
At least five Somali policemen were killed in a roadside bomb blast in the south of the capital on Monday.
A moderate Islamist president took office in January but even his introduction of Sharia law to the strongly Muslim country has not appeased the guerrillas, who are accused of links to al-Qaeda.
There are 4,300 African Union peacekeepers from Uganda and Burundi in the capital to help bolster the government, but they do not have a mandate to pursue the insurgents.
It is estimated at least one million people have been internally displaced by almost perpetual civil conflict in the country since the collapse of its central government in 1991.
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