Speaking on state television after his swearing-in ceremony, Mr Abiy called for an end to “years of misunderstandings”.
“I call on the Eritrean government to take the same stand,” he said.
Mr Abiy – who was chosen to lead the ruling coalition after the unexpected resignation of Prime Minister Hailemariam Desalegn in February – 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.
But Eritrea’s information minister Yemane Gebre Meskel say any progress on a peace plan cannot proceed until Ethiopia withdraws “from the occupied territories”.
“The ball has stayed for too long in Ethiopia’s court. There is no dispute as the litigation process ended 16 years ago. Ethiopia needs to honour its treaty obligations and respect Eritrea’s sovereignty and territorial integrity by withdrawing from occupied territories – including Badme.
“Peace will indeed be beneficial to the two peoples but obviously, this must be predicated on respect of international law which Ethiopia continues to flout to date,” Meskel stressed.
The two countries have had poor relations since a two-year border war, which claimed 70,000 lives.