Rice is meeting African leaders amid growing US unease concerning worsening security and failing peace deals in a number of countries on the continent.
Ethiopia sent troops to Somalia late last year to support the transitional government against the Islamic Courts Union which controlled large areas of the country. It is not part of the AU force.
"She [Rice] could actually achieve a whole lot if she wanted to. The most important issue right now in Ethiopia is the severely deteriorated situation in Somalia, where massive human suffering continues to intensify," Salim Lone, Africa analyst and columnist, told Al Jazeera.
"War crimes are being committed, civilian communities are being targeted, journalists are being killed [and] food is being withheld from areas that are considered hostile to the government. This must change."
Lone said that the situation of in Somalia had been of the "United States' making" and that it should change its strategy for the region.
Rice, who is the first US secretary of state to visit Africa in a decade, is scheduled to meet Somalia's new prime minister during her trip.
Five ministers in the Somali government resigned this week, soon after the cabinet was named, in protest at what they see as lack of representation for their respective clans.
Rice said that the Somali prime minister had to be more inclusive in his administration.
"The Somali leadership is going to have to really reach out to all the elements that are not associated with terrorism," Rice said.
"It has to be broad and that's really my message to the prime minister. He has to find a way to broaden his base of support."
|"The Somali leadership is going to have to really reach out to all the elements that are not associated with terrorism"|
Condoleezza Rice, US secretary
Ethiopia invaded Somalia in December 2006 to battle fighters loyal to the Islamic Courts Union (ICU), who had taken control of the south of the country from the government.
Although the Islamic movement was defeated by Ethiopian forces its supporters are now leading the fighting against the government.
Nearly 6,000 civilians have been killed in the crossfire this year, according to a Somali human right group.
Rice is also due to hold talks with Meles Zenawi, Ethiopia's prime minister, whose country shares a tense border with rival Eritrea.
"We don't need a use of force here to deal with what is obviously a significant border problem," Rice said on her way to Addis Ababa.
Tens of thousands of people were killed during a 1998-2000 Ethiopian-Eritrean war, and the border issue remains unresolved after a border commission ended its mandate on Saturday.
DR Congo talks
In her first meeting on Wednesday, Rice met leaders from Burundi, Rwanda, Uganda and the Democratic Republic of Congo to discuss the conflict in eastern DR Congo.
Fighters following Laurent Nkunda, a renegade Congolese general, have been fighting UN-backed government forces in the area.
Rice said dealing with the rebels is critical to re-establishing normalcy in a region that has been devastated by decades of war and genocide that have killed millions.
|Rice also discussed Congo, where rebel general|
Nkunda is fighting UN-backed forces [AFP]
"We had a very thorough discussion," Yoweri Museveni, Uganda's president, said.
"Part of the danger in Africa is handling issues in a superficial way."
Tens of thousands of people have fled from violence in eastern DR Congo recently, straining humanitarian resources in the region.
Rice said she would also focus on the Darfur conflict in Sudan on her trip, in an attempt to support a faltering peace deal that ended Sudan's north-south civil war.
She said the US wants a joint UN-AU peacekeeping force to be deployed in Darfur.
Sudan's government and Arab Janjiwid fighters have been accused of killing thousands of black Africans living in Darfur.