But with the region cut off to the outside world, DW has been unable to independently verify the Ethiopian government's claims.
The Tigray People’s Liberation Front (TPLF), which rules the northern state of more than 5 million people, has not commented on the statement.
Abiy, who at 44 is Africa’s youngest leader, has so far resisted calls by the United Nations, the African Union and others for an immediate cease-fire and negotiations.
Also on Thursday, Ethiopia's parliament stripped 39 of its members, including the Tigray regional president Debretsion Gebremichael, of immunity from prosecution, according to a report by the country's state news agency.
Fighting could spread
There are widespread concerns that the fighting in Tigray could spread to other parts of Africa’s second-most-populous country, and to the rest of Horn of Africa region.
Once the country's most powerful party, the Tigray People's Liberation Front (TPLF) that rules the Tigray region has been feuding with Prime Minister Abiy since he came to power in 2018 and promised reform nationwide.
The TPLF recently ignored a national ban on elections due to coronavirus. Abiy responded by calling their regional vote illegal.