Trip by paramilitary groups leader comes a week after his forces captured North African nations second largest city.
Mogadishu says a deal to grant Addis Ababa access to sea in Somaliland is a violation of its sovereignty.
The deal will pave the way for the landlocked country to use the port of Berbera.
Addis Ababa insists the dam will not harm its neighbours as another meeting is held with Egypt and Sudan.
We should be careful not to repeat the mistakes made in Sudan.
The countries have a long history of getting involved in each others affairs, leading to fears of a regional crisis.
Addis Ababa is concerned as the war next door shows no sign of ending.
Sudans second most powerful leader Mohamed Hamdan Daglo is in Addis Ababa on a two-day visit.
US envoy, assistant secretary to meet leaders and civil society actors during severe crises in the two African nations.
Humanitarians sound alarm over growing humanitarian crisis amid challenges to provide aid to those fleeing conflict.