"We have moved one step forward. We have discussed, agreed and signed. The next thing expected from us will be to implement honestly what we have promised to make the peace sustainable," Abiy told Ethiopia's national parliament after hearing questions from lawmakers.
The truce, signed November 2, agreed to end two years of war that has devastated the Tigray region, killing thousands, displacing millions and threatening the unity of Africa's second-most populous nation.
Abiy's government and representatives from Tigray on Saturday signed a further deal for implementing the ceasefire.
Under the implementation deal, the parties pledged to allow unhindered humanitarian aid into Tigray -- international aid is still to reach the war-ravaged region nearly two weeks since the ceasefire.
The deal also made it explicit that disarmament would happen alongside foreign and other forces, excluding the Ethiopian army, withdrawing from the region.
Abiy said on Tuesday that a territorial dispute between forces in Tigray and the neighboring Amhara region should be resolved legally and through discussion.
Authorities in Amhara last week welcomed the ceasefire agreement but made no mention of the disputed territory.
Fighters from Amhara entered western Tigray in November 2020 in support of federal troops and took control of a swathe of territory they say was historically theirs. Tigrayan officials say the area has long been home to both ethnic groups.
The war, which has pitted Abiy's government against the Tigray People's Liberation Front - the party which dominates the region - is rooted in old grievances between the political elites of ethnically-based regions, built up over decades of turmoil, violent regime change, territorial disputes between regions and long periods of authoritarian rule.
