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A regional force which backed the Ethiopian government in its brutal two-year war against Tigrayan rebels has withdrawn from a strategic city in Tigray, the army said on Thursday.

It said the pullout by the Amhara special forces from Shire followed Wednesday's announcement by the Tigray People's Liberation Front (TPLF) that it has begun surrendering its heavy weapons.

The moves are a key part of a November peace deal between the federal government and the TPLF to end the conflict in northern Ethiopia that has claimed untold numbers of lives.

"Today, the Amhara special force which had been undertaking a national mission [in Shire] with the defence force has left the area as per the agreement," the federal defence force said in a statement posted on Facebook.

Under the agreement between the once warring sides, foreign forces and those that are not part of the Ethiopian national army were to withdraw "concurrently" with the rebel disarmament.

Residents and aid workers have reported the presence of both Amhara forces and Eritrean troops in Shire and other parts of Tigray, accusing them of atrocities including murder, rape and looting.

A withdrawal of Eritrean troops, who played a key role on the battlefield backing Ethiopian government forces, has long been a demand of the Tigrayan rebels as well as Western governments.

But the peace deal makes no specific mention of the Eritrean army.

Access to Tigray remains restricted to journalists and it is not possible to independently verify the situation on the ground.