The UN accused both sides in the conflict of breaking humanitarian law by indiscriminately firing on civilian areas.
Up to 18,000 refugees from Mogadishu have ended up in a district called Bulla Hawa on the Somali-Kenyan border.
Most of them hope to cross into the already overflowing refugee camps in Kenya, but even that murky oasis is out of reach as the border has been closed.
Mohammed Adow, Al Jazeera's correspondent in Bulla Hawa, said the refuges lived in desperate conditions in the lawless town.
Nimo Billow, one of the refugees, said: "I decided to flee Mogadishu with my children when our neighbours' houses were hit by mortars and rockets.
"It was a sudden decision and even my husband was not at home when we fled. The market where he works was hit my mortars the same day we fled. We still have no information on his whereabouts."
The refugees are putting more pressure on an already impoverished community.
An outbreak of cholera in the area has killed dozens and left hundreds seriously ill.
|Nimo Billow, left, and her children fled after|
her neighbourhood was bombed
The frontier town, like many parts of Somalia, remains chaotic and unsafe, with militias ruling and gun battles common.
Abdullahi Yusuf, the Somali president, said last month that his pro-government forces had won the battle in Mogadishu and the fighting was over. He urged residents to return to their homes.
"I urge residents in Mogadishu to return to their homes... We, the government, regret fighting in residential areas and forcing them to flee their homes," he said.
But many refguees do not appear to be heeding his call.
Despite the poor conditions in areas like Bulla Hawa, most will not return to Mogadishu but hope for help to reach them.
"Despite all my problems here I do not intend to go back to Mogadishu anytime soon," Billow said.
The International Committee of the Red Cross on Tuesday appealed for more than $15m for Somalia.
The move would bring the Red Cross' budget for Somalia to nearly US$38m for 2007.