Residents say, heavy weaponry is being used. There are also fears that civilians are trapped.
The authorities had claimed they had contained the conflict but, fighters from the Fano militia group say, they have thwarted government attacks and seized towns.
Communications blackouts have been imposed, making it difficult to confirm the details of the violence.
The Ethiopian government announced a state of emergency in August, when the Fano militia refused to hand over its weapons.
Last week, Western countries including Britain and the US, called for a ceasefire.