The Ethiopian army has launched co-ordinated attacks on all fronts against forces from the northern Tigray region, the rebels say.
They said the government was using artillery, tanks, jets and drones in an attempt to “reinvade” the region.
A senior rebel source said Tigray forces were holding their ground.
The Ethiopian government has not confirmed any fighting, and a communications blackout makes independent verification impossible.
A senior member of the Tigray People’s Liberation Front (TPLF), Getachew Reda, said the government offensive launched last week was now in “full swing”.
Asked if a ground offensive had been launched, 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 but gave no further details.
The 11-month conflict has caused a humanitarian crisis, with the United Nations warning that about 400,000 people were living in famine-like conditions in Tigray in July.
Thousands of people have been killed in the conflict, and another two million have been forced to flee their homes.