Reuters was not immediately able to verify the account on Twitter from Getachew Reda, a spokesman for the Tigray People's Liberation Front (TPLF).
"Eritrea is deploying its entire army as well as reservists. Our forces are heroically defending their positions," Getachew said.
Eritrean Information Minister Yemane Gebremeskel did not immediately respond to requests for comment.
If confirmed, the offensive would mark an escalation in a war that has already displaced millions and triggered a humanitarian disaster across northern Ethiopia.
Getachew said Ethiopian troops and special forces from the Amhara region to the south had also joined the offensive.
Eritrean troops entered Tigray to back the Ethiopian military after fighting broke out in November 2020 before withdrawing from most areas last year.
Ethiopian government spokesperson Legesse Tulu, military spokesperson Colonel Getnet Adane and the prime minister’s spokesperson Billene Seyoum did not immediately respond to requests for comment.
Gizachew Muluneh, spokesperson for the Amhara regional government, also did not immediately respond to a request for comment.
Eritrea's Yemane confirmed over the weekend that some reservists were called up but said the government was not mobilising the entire population.
The conflict in Tigray re-erupted on Aug. 24, breaking a ceasefire in place since March. Earlier this month, Tigrayan forces said they were ready for a ceasefire and would accept an African Union-led peace process.
