Eritrea reopened its embassy in Ethiopia on Monday in further evidence of a rapid thaw between two countries that a week ago ended two decades of military stalemate over a border war in which tens of thousands of people died.

Ethiopia's Prime Minister Abiy Ahmed and Eritrea's President Isaias Afwerki re-opened the embassy in the capital Addis Ababa in a brief ceremony, a Reuters witness said. One week ago the leaders declared their "state of war" over and Isaias spent the weekend in Ethiopia.

The rapprochement could help Ethiopia, a landlocked country of 100-million people with the largest economy in East Africa, by making access to Eritrea's ports possible. Better ties could help Eritrea overcome decades of relative isolation.

The leaders jointly raised the Eritrean flag inside a newly refurbished embassy as a military band played Eritrea's anthem. They then toured the building and looked at its furniture and two rusting cars that belonged to Eritrea's last ambassador.

In a tweet Eritrea's information minister, Yemane Meskel described the reopening of the embassy as "yet another milestone in the robust and special ties of peace and friendship both countries are cultivating with earnestness in these momentous times."

Isaias left Addis Ababa to return home soon after re-opening the embassy.

The Eritrean leader arrived in Addis Ababa for a three-days visit on Saturday and thousands lined the Ethiopian capital's main thoroughfare Bole Road, sporting T-shirts emblazoned with the pictures of both countries' leaders.

Eritrea formally seceded from Ethiopia in 1993 after a long battle for independence, but the two fought a border war in 1998 that claimed lives of at least 80 000.

A peace deal was signed two years later but Ethiopia refused to implement it, saying it wanted more talks.

The armies of both nations have both been facing off across their border since the war ended and security dominates both countries concerns.

The rapprochement was set in motion after Abiy in April became Ethiopia's prime minister. Abiy said he would accept and implement a boundary commission's ruling on the Eritrea border and implement sweeping political and economic reforms.

Abiy's chief of staff, Fitsum Arega, said in a tweet better ties "will create the ideal conditions to address remaining strategic issues in the shared interest of the two nations."