Somalia's transitional government should hold talks with moderate members of the country's Islamist movement, the US ambassador to Kenya has urged.
Ethiopia has said its troops will not remain in Somalia
Michael Ranneberger told the BBC that the government needed to engage with all elements of Somali society.
Government troops backed by Ethiopian soldiers ousted the Union of Islamic Courts (UIC) from power late last year.
On Saturday four people thought to be civilians died in a crossfire as gunmen attacked an Ethiopian military convoy.
The incident, in the south of Mogadishu, followed an attack on the presidential palace late on Friday, which prompted many residents to flee.
The US has been among those accusing the Islamic courts of harbouring al-Qaeda suspects, claims the UIC's leaders deny.
But Mr Ranneberger told the BBC that among extremists there were moderate elements who should be included in dialogue.
He named the co-figurehead of the organisation, Sheikh Sharif Sheikh Ahmed.
"Anyone inside Somalia who renounces terrorism, extremism and violence, should have a role to play in the future of the country," he said.
"To the TFG [transitional government] this means that they should be reaching out to talk to all elements of Somali society."
"We certainly have made clear to the TFG that it needs to talk to all elements and that includes people such as, for example, Sheikh Sharif, who was considered a moderate member of the Islamic Courts."
Somalia's Islamists were routed in an offensive by Ethiopian and Somali government troops at the end of 2006.
The Union of Islamic Courts had swept over much of southern Somalia last year, capturing Mogadishu in June.
In Saturday's attack on the Ethiopian convoy, gunmen fired light machine guns and possibly rocket-propelled grenades, but missed, reports said.
The Ethiopian troops then retaliated and a man and a woman by the side of the road were killed.
Two other people who were wounded died on the way to the hospital, medical officials told the AFP news agency.
There were conflicting reports about whether those who died were killed by the attackers or by the Ethiopians returning fire.
Somalia's Ethiopian-backed interim government says some 3,500 Islamist fighters remain in hiding in Mogadishu.
But Ethiopian Prime Minister Meles Zenawi told the BBC on Friday his troops would start leaving Somalia "in the next few days".
African Union peacekeepers are due to head for Somalia, although Uganda is the only country to have offered to send troops to replace the Ethiopian soldiers.
Three battalions are due to be sent initially, with six more battalions to follow.