"We are undertaking a massive manhunt as we have been given details of what the bomber looked like."
Tamrat added that the first bomb detonated in a hotel named Kidane Mihret and the second in Shuferoch hotel, a few yards away.
Zemedkum Tekle, an information ministry spokesman, said that "terrorists" were responsible for the bombings, without giving further details.
For years there has been conflict in Ethiopia's Oromo region, where opponents to the government claim they have been marginalised.
On May 20, a bomb exploded on a minibus in Addis Ababa, killing six people.
Police blamed that attack on the Oromo Liberation Front who they said were financed by neighbouring Eritrea.
Eritrea denies any involvement.