Co-ordinated attacks on all fronts against forces from northern Tigray region has been launched by the Ethiopian army, the rebels said.
Artillery, tanks, jets and drones was used by the government to “reinvade” the region they said.
A senior rebel source said Tigray forces were holding their ground.
The government offensive launched last week was now in “full swing”, said Getachew Reda, a senior member of the Tigray People’s Liberation Front (TPLF).
Ethiopian Prime Minister Abiy Ahmed’s spokeswoman Billene Seyoum said the government had a responsibility to protect its citizens across the country from acts of terrorism. She gave no further details.
The Ethiopian army took control of most of Tigray in November 2020, after the Tigray Peoples Liberation Front (TPLF) forces backed by Eritrean troops seized a military base.
In a surprise attack, the rebels in June recaptured Tigray and then moved into parts of neighbouring regions like Amhara.
Ethiopia has declared the TPLF a terrorist organisation, but the TPLF insists that it is the legitimate government in Tigray.
The 11-month conflict has led to the death of thousands of people, and another two million have been forced to flee their homes.
In July, the United Nations warned that the humanitarian crisis has caused famine-like living conditions for about 400,000 people in Tigray.