"The second phase of Ethiopian troop withdrawal should be completed within 120 days," the agreement said, although Price was unable to say when exactly the countdown would begin.
Ethiopian forces were deployed to Somalia to help government troops force out the Islamic courts union, which controlled Mogadishu and much of southern and central Somalia.
However, it was unclear how succesful the deal, which comes before efforts to restart peace talks in the Kenyan capital Nairobi, would be in tackling the violence as al-Shabaab, which has carried out a series of attacks, and several other armed groups were not represented in Djibouti.
In the latest violence, six people died when Ethiopian and Somali forces clashed with anti-government fighters after their military convoy was ambushed near the town of Baidoa.
A witness said that the fighters used "mortars and machine-gun fire" to attack nine government vehicles. A second witness said nine Somali soldiers were taken to hospital.
In Wanlaweyn, about 90km south of Mogadishu, the bodies were of four civilians were found after another clash between Ethiopian forces and fighters.
Two police officers and a civilian alo died when a roadside bomb exploded near a police checkpoint in the north of the capital, according to police.
More than 10,000 people have been killed and one million other displaced by the fighting since early last year.