Ethiopia's Tigray region on Tuesday welcomed the first international aid delivery since a truce to end fighting, with the International Committee of the Red Cross (ICRC) driving two medical trucks to the capital of the war-ravaged area.

Ethiopian Prime Minister Abiy Ahmed's government and Tigrayan forces signed a cease-fire on November 2 to end two years of fighting that have killed thousands, shattered infrastructure and uprooted millions from their homes.

Implementation includes unhindered access for aid to a population facing disease and famine.

"It is an enormous relief for us to deliver this cargo," Nicolas Von Arx, head of the ICRC delegation in Ethiopia, said in a statement. "The health care system in the region is under extreme pressure and these deliveries are a lifeline for people who need medical help."

The ICRC described the delivery into the regional capital Mekelle as the first international aid into Tigray since a previous cease-fire broke in August.

Ethiopia's government has also begun supplying some aid.

Half of the region's 5.5 million people are in severe need of food. Aid agencies say they will not know the true extent of needs until they can access areas for the first time in months.

"We have moved one step forward. We have discussed, agreed and signed," Abiy told Ethiopia's national parliament in his first comments on the cease-fire since it came into force. "The next thing expected from us will be to implement honestly what we have promised to make the peace sustainable."

A deal for implementation of the cease-fire signed on Saturday made it explicit that disarmament would happen alongside foreign and other forces, excluding the Ethiopian army, withdrawing from the region.

Troops from neighboring Eritrea, as well as forces from other Ethiopian regions, have fought on the side of the Ethiopian army.

Abiy said on Tuesday that a territorial dispute between forces in Tigray and the neighboring Amhara region should be resolved legally and through discussion.

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.