Regional leaders welcomed the peace efforts with Rwanda's President Paul Kagame telling Abiy and Isaias, "We congratulate you and are with you", in a Twitter statement.
"[The prime minister] is expected to talk with the Eritrean leadership on how to mend fences".
Ethiopian and Eritrean leaders have formally restored relations between the two countries, ending 20 years of enmity and prompting phone calls across the border by people getting back in touch with friends and family.
Eritrea achieved independence from Ethiopia amicably in 1993 but the two countries swiftly became bitter enemies.
The Algiers agreement came after the two neighbors fought a bloody war from 1998-2000 in which 70,000-80,000 people perished on both sides.
"This historic official visit, and the summit that will take place. heralds a new era of peace and cooperation", Eritrea's Information Minister Yemane Gebremeskel wrote on Twitter. "The summit would, set the tone for rapid, positive changes on the basis of respect of sovereignty & territorial integrity, equality and mutual interest of both countries", he wrote.
A direct worldwide telephone connection between the two countries was restored "for the first time after two decades", he wrote.
Ethiopia's young reformist leader, Abiy Ahmed, flew into the capital of Eritrea on Sunday morning for a visit that stunned people in the two countries.
Nadal progresses into last 16
Williams will follow Federer at Centre Court, and she plays 120th-ranked qualifier Evgeniya Rodina of Russian Federation . Keys also came up short with a comeback attempt after fighting back from a set and two breaks down, losing 7-5, 5-7, 6-4.
Ethiopia's state-owned airlines will resume flights to Eritrea's capital Asmara next week, a state-affiliated news agency reported on Monday, hours after the neighbours and longtime foes declared their "state of war" over.
In early June, Ethiopia announced it would honor all the terms of the 2000 peace deal, suggesting it might be ready to settle the border dispute.
Eritrea responded positively, sending a delegation to Addis Ababa last month.
"We agreed that the airlines will start operating, the ports will be accessible, people can move between the two countries and the embassies will be opened", Abiy said at a dinner hosted by his Eritrean counterpart.
Ethiopian access to Eritrea's ports will be an economic boon for both, as well as posing a challenge to the increasing dominance of Djibouti which had benefitted from importing and exporting the vast majority of goods to Africa's second-most populous country.
In office since April, Abiy has pursued an ambitious reform agenda, including reversing years of policy and announcing that Ethiopia would abide by the 2002 boundary ruling.
The announcement promised to end of one of Africa's most intractable military stand-offs, a conflict that has destabilized the region and seen both governments funnel large parts of their budgets into security and soldiers.
However, it has also attracted opposition from hardliners in the Tigrayan People's Liberation Front (TPLF), the ethnic Tigrayan party that has dominated the ruling EPRDF coalition - and by association the country and economy - for almost three decades.
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