In this file photo Tigray People s Liberation Front (TPLF) fighters arrive after eight hours of walking in Mekele, the capital of Tigray region, Ethiopia, on June 29, 2021. AFP
"These invading forces have taken control for the moment of some areas including Shire," the Tigray Central Command said in a statement, adding that the rebels were in a "life or death" struggle.
It said the joint forces had entered the city of about 100,000 people on Monday, adding: "The enemies are massacring our people with heavy weaponry/armaments in the areas it invades."
The Shire area had been the scene of an offensive by Ethiopian and Eritrean troops as intense fighting was reported in Tigray, triggering deep alarm in the international community.
It is not possible to verify battlefield claims as Tigray is under a communications blackout and access to northern Ethiopia is restricted for journalists.
UN chief Antonio Guterres warned Monday that the situation in Ethiopia was "spiralling out of control" as the fighting raged.
The rebel announcement came a day after the Ethiopian government vowed to seize airports and other sites in Tigray.
The African Union had called on Sunday for an immediate and unconditional truce as the combat intensified between pro-government forces and the Tigray People's Liberation Front who have been at war for nearly two years.