Date: Monday, 02 April 2018
Speaking on state television after his swearing-in ceremony, Mr Ahmed called for an end to "years of misunderstandings".
"I call on the Eritrean government to take the same stand," he said.
The two countries have had poor relations since a two-year border war, which claimed 70,000 lives.
Mr Ahmed was chosen to lead the ruling coalition after the unexpected resignation of Prime Minister Hailemariam Desalegn in February.
He is Ethiopia's first Oromo leader - an ethnic group which has led anti-government protests for three decades.
State television channel ETV broadcast his speech live after he was sworn in.
Mr Ahmed said the country was ready to resolve differences between the two peoples, who are "not only intertwined in interests but also in blood".
"We will stand by our African brothers in general and our neighbours in particular, during good and bad at times," he said.
Mr Desalegn, while in power, had accused Eritrea of backing anti-government protests in the country.
Ethiopia still occupies land at the heart of the conflict, around the town of Badme.