The first high-level Eritrean delegation to visit Ethiopia in decades has arrived for a meeting which could ease military tension.
Eritrea won independence from Ethiopia in 1993 after a 30-year conflict - but a border war five years later killed tens of thousands.
Diplomatic ties have been cut between the two countries for almost 20 years.
Last week, Ethiopia's prime minister said he would accept a peace deal awarding Eritrea disputed territory.
The deal, agreed by a border commission in 2002, had never formally been accepted by Ethiopia.
It is just one of a series of reforms Abiy Ahmed, who became prime minister after his predecessor resigned in February, has enacted since he took power.
On Sunday, a political rally he attended was hit by a grenade blast which killed two people and injured dozens, though Mr Ahmed was uninjured.
On Monday evening, Reuters quoted Eritrean Foreign Minister Osman Saleh as saying "We have opened the door of peace," after the first talks.
Speaking for Ethiopia, Mr Abiy said: "Let this dispute conclude with this generation. Let the era of love and reconciliation commence."
The Eritrean delegation, led by Mr Saleh, was welcomed earlier on Tuesday by Mr Abiy in the capital Addis Ababa, where a red carpet was rolled out and the visitors were offered garlands of flowers.
Ethiopian elders, religious figures and traditional dancers were all part of the welcoming committee.
In the streets of the capital, a poster showing both flags together with a message of welcome hung from buildings.
Writing on Twitter, Mr Abiy's chief of staff said the prime minster "hopes the visit will lay the foundation for a much brighter future for Ethiopia [and] Eritrea".
"It is wonderful to see an Eritrean delegation in Ethiopia," one Eritrean man living in Kenya told the BBC.
"I can't explain my emotions. I am happy to be alive to witness the peace process resuming," Deacon Daniel Bahlbi said.
"Of course there are many problems in both countries and if this situation is solved amicably, all of us will benefit."
A major step for warring neighbours
Analysis by BBC Monitoring
The arrival of an Eritrean delegation to Ethiopia is a major step towards mending relations between the Horn of Africa neighbours.
The countries have been on a war footing, despite a peace agreement almost two decades ago.
While Ethiopia has gone on to forge close ties with the US on counter-terrorism operations, Eritrea became reclusive.
The main issue has been Eritrea's demand for Ethiopia to unconditionally accept the 2002 boundary commission's ruling, including withdrawing its troops from Badme.
Ethiopia's indicated earlier this month that it will cede disputed territory, and the Eritrean delegation will want a firm commitment in this regard.
The visit comes days after a blast in Addis Ababa targeting a rally attended by the prime minister. Eritrea condemned the blast, in what could be seen as a statement of support for Mr Abiy, who is facing some opposition within the ruling coalition to his peace plan.
The peace agreement of 2000 calls for the end of hostilities between the two countries and to respect the ruling of the UN border commission, which delivered its verdict in 2002.
Ethiopia struggled to accept the decision, however, when the proposed border awarded Eritrea disputed territories that included the town of Badme - a key site in the 1998-2000 border war.
The effect of the continuing dispute has been that both nations remained prepared for war for almost 20 years.
Border skirmishes - involving both national forces and rebel groups - have continued sporadically ever since, while Badme has remained under Ethiopian administration.