A US envoy said they were aware of Eritrean troops crossing into Tigray and condemned the movement, while the Eritrean and Ethiopian governments have not yet commented on the claims.
If Eritrea's offensive against the rebels is confirmed, it will mark an escalation following the collapse of a five-month truce last month.
Eritrea intervened on the side of the Ethiopian military, but it reportedly withdrew most of its troops last year.
On Tuesday, TPLF spokesman Getachew Reda said heavy fighting was taking place in several areas along the Tigray-Eritrea border.
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