"The men, who were said to be in two vehicles, attacked with machineguns and lobbed grenades and, according to witnesses, also used anti-tank missiles.
"Somali government forces who were guarding the Ethiopian base engaged the attackers in a gun battle. No casualties have been reported on the Ethiopian side.
"A 13-year-old girl is said to have died after getting caught in the crossfire. And a man is now recuperating in a Mogadishu hospital after being injured."
All this is happening at a time when the Somali government is trying to establish its rule in the capital, Adow said, adding that the hand of "remnants of the [Council of] Islamic courts is suspected".
A Somali transitional government source said: "The insurgents came with two vehicles and opened fire at government forces holding defences outside a compound where the Ethiopian soldiers are staying.
"The Ethiopians were inside. Fighting ensued. Heavy fire was exchanged; one anti-tank rocket was launched by the insurgents."
Also on Sunday, in the south-central town of Baladweyne, hundreds of poeple took to the streets demanding that Ethiopian troops free a military commander detained for refusing to hand over an Islamic courts member despite a government amnesty offer to the defeated movement.
Al Jazeera's Adow said the clashes resulted in the death of one person and injuries to several others.
The violence came after Ali Mohamed Gedi, prime minister of the Somali transitional government, and Jendayi Frazer, Washington's most senior diplomat for Africa, met in the Kenyan capital, Nairobi, on Sunday.
Jamae Nur Ahmed, another Al Jazeera correspondent in Mogadishu, said Frazer cancelled a planned visit to the Somali capital owing to the precarious security situation.
Frazer flew directly to Nairobi to meet Gedi and representatives of the civil society, Jamae Nur said.
Somali policemen patrolling the streets of
Mogadishu, the once lawless capital [Reuters]
The government, which was confined to the provincial town Baidoa, now wants to install itself in Mogadishu.
Frazer has been travelling around the region as Western and African diplomats discuss an African peacekeeping force for Somalia after two weeks of war during which Ethiopian and government troops forced out the Islamic courts militia, which had captured much of the south.
Frazer said Washington was donating $16m to help fund the proposed force and she has called for dialogue between Somali groups, including "remnants" of the Islamic courts.
After meeting Frazer, Gedi said: "We are going to work together for the stabilisation of Somalia."
For his part, Abdullahi Yusuf, the Somali president, has asked Ethiopia to train Somali forces, Ethiopian state television said on Saturday, after he met Meles Zenawi, the Ethiopian prime minister.
Zenawi has said Ethiopian soldiers will leave Somalia within weeks.
In other news, Abubakr al-Qirbi, the Yemeni foreign minister, has been quoted as saying that some Islamic courts leaders had arrived in Yemen, creating an opportunity for talks with Somalia's government.