Ethiopian troops are leaving after two years in Somalia
The African Union has agreed to keep its peacekeeping force in Somalia for a further two months.
But the AU's peace and security council appeared to make little progress on the problem of replacing Ethiopian troops when they leave at the end of the year.
Ethiopia has rejected pleas to phase its withdrawal in co-ordination with the arrival of fresh forces.
The AU force already in Mogadishu is too small to resist resurgent Islamist and nationalist fighters.
UN Secretary-General Ban Ki-moon last week rejected calls for UN peacekeepers to be sent.
He said the situation in Somalia was too dangerous and there was no peace to keep.
Appeal for troops
The African Union "discussed in depth the situation in Somalia and decided to prolong the mandate of the mission on the ground for two months," spokesman El Ghassim Wane told the AFP news agency.
He admitted the AU was "conscious of the challenges which will result" from the loss of Ethiopia's 3,000 troops.
And he said the organisation, at its meeting in the Ethiopian capital Addis Ababa, had "reiterated its appeal to member states to furnish the necessary troops" to the peacekeeping mission.
The AU force currently comprises 3,400 soldiers from Uganda and Burundi - limited to parts of Mogadishu and the central town of Baidoa, where parliament is based.
Nigeria, Uganda and Burundi have said they could each send a battalion - about 850 troops.
But to get them there will require money and logistic support from outside Africa, which is difficult to organise in two weeks especially over the festive period, the BBC's Elizabeth Blunt in Addis Ababa says.
There is almost certainly going to be a period when the present small force will be left to manage on its own, and it will have to do this on its existing, purely peacekeeping, mandate, our correspondent adds.
Somalia has not had a functioning national government since 1991.
Ethiopian troops intervened two years ago to oust Islamists from the capital and install the internationally-recognised government.
Islamist insurgents are taking over more of Somalia
But that government is now in disarray and different Islamist groups now control much of southern Somalia.
The UN envoy to Somalia, Ahmedou Ould Abdallah, on Monday described the country's problem as a "problem for the whole region".
"There is a hidden genocide in Somalia which has sacrificed entire generations," he was quoted by AFP as saying.
Fighting between pro-government forces and Islamist militias has led more than a million people to flee their homes.
The lack of an effective government has led to the rise of piracy off the Somali coast.
Aid agencies say some three million people need food aid - about a third of the population - but attacks by pirates and militias make it extremely difficult to deliver humanitarian assistance.