Ethiopia's national army has captured three towns in the northern region of Tigray, where it has been battling regional forces on and off for two years, the government said on Tuesday.

The conflict pitting the Ethiopian military and their allies, who include Eritrean troops, against the Tigray forces has killed thousands, displaced millions and left hundreds of thousands on the brink of famine.

"The ENDF (Ethiopian National Defence Force) has taken control of the towns of Shire, Alamata, and Korem without fighting in urban areas," Ethiopia's government information service said in a statement.

A spokesperson for the Tigray forces did not immediately respond to a request for comment.

Earlier, the Tigray authorities had acknowledged losing control of Shire, one of the region's biggest towns which hosts ten of thousands of people who were displaced from other areas by the conflict.

The United Nations human rights office said it was concerned that some air strikes by government forces in Tigray had been indiscriminate.

In its statement, the government said the national army was taking "maximum care" to protect civilians from harm.

The government will coordinate preparations with humanitarian groups to bring aid and restore services to areas now under its control, the statement added.

The Tigray conflict is rooted in long-running rivalries between regional power blocs over control of Ethiopia as a whole and in deep disagreements over how power should be balanced between federal and regional authorities.

The United Nations, the European Union and several senior US government officials have all called in recent days for an immediate ceasefire, for the launch of African Union-sponsored talks and for the withdrawal of Eritrean troops from Ethiopia.