Eritrean troops have suffered "heavy losses" and are retreating towards their border, a spokesperson for an Ethiopian pro-government militia told AFP on Tuesday.
Meanwhile, Ethiopian federal forces and their allies were closing in on a town near Eritrea's border on Wednesday, according to a pro-government militia commander and a resident, raising fears of a regional war.
Ethiopia accuses Eritrea of backing the rebel Tigray People's Liberation Front (TPLF), which launched a major offensive against government forces on September 23 before being pushed back and losing control of its strongholds.
A foreign security source has estimated that between 5,000 and 8,000 Eritrean forces were deployed in Ethiopian territory to support the rebels but were also forced into an apparent retreat.
"The Eritrean army crossed into Ethiopia and violated its sovereignty, but it has suffered heavy losses and retreated towards the border," Solomon Hailemariam, spokesperson for the Tigray Peace Force, a pro-government militia, told AFP.
AFP was unable to independently verify this information.
Eritrean Information Minister Yemane Gebremeskel told AFP the pro-government militia was "not trustworthy". He also dismissed rumours of Ethiopian troops crossing the border, calling them "absolutely false".
The rebel TPLF once controlled the whole of Ethiopia but lost power with the rise of Prime Minister Abiy Ahmed, who hails from the Oromia region, in 2018.
It remained in control of the northern state of Tigray and fought a brutal civil war against Abiy's federal government from 2020 to 2022 that was never fully resolved.
'Avoid escalation'
With the government counter-offensive over the past fortnight, the TPLF lost control of the Tigrayan capital, Mekelle, and other towns and cities.
"The TPLF is no longer in a position to stand and fight, we have either seized or destroyed its weapons," the pro-government militia spokesperson said.
He said pro-government forces were now gathered in areas bordering Eritrea.
The International Crisis Group, an NGO, warned on Monday that Ethiopia and Eritrea were "perilously close to all-out war" as clashes drew nearer the border.
It urged the international community to "press both sides to avoid escalation".
Eritrea gained independence from Ethiopia in 1993 and they fought a border war from 1998 to 2000.
They briefly mended relations when Abiy came to power, but have again fallen out, and severed relations entirely this month over the Tigrayan conflict.
Eritrea accuses landlocked Ethiopia of planning to use the conflict as a justification to invade its territory and seize control of Assab port on the Red Sea.