Eritrea says its forces evacuated from the town.
The latest clashes in the two-year border war comes as Ethiopia is considering its approval of a ceasefire proposal put forward by the Organisation of African Unity and already accepted by Eritrea.
Ethiopian forces first took Tesseney in early June, but Eritrean forces recaptured the town on 6 June.
Ethiopia said at the time that it had voluntarily withdrawn, but journalists saw the bodies of dozens of Ethiopian fighters in the town and evidence of heavy fighting.
Eritrea meanwhile has said that there has been shelling near the southern port of Assab.
According to the ceasefire plan the Ethiopians are to pull back from the positions they now occupy within Eritrea, and a UN force will be deployed in a buffer zone on the Eritrean side of the pre-war border.
Concerns
Diplomats are said to be cautiously optimistic that Ethiopia will sign up to the proposal, and an announcement is expected soon.
But our correspondent says continued fighting, especially around Assab, raises concerns that landlocked Ethiopia wants to take the Eritrean port before any cessation of hostilities.
The continued fighting in Western Eritrea could also complicate efforts to feed at least 9m people in both countries who are threatened by hunger.
The rainy season is expected within the next two weeks, but areas scheduled for intensive mechanised farming in the west are now the scene of fighting.
Eritrea is not self-sufficient in food production, even in good years, and without a good harvest the country, like Ethiopia, will be in desperate need of emergency assistance.
The Organisation of African Unity, which is brokering the indirect peace talks in Algiers, said it expected the two sides to sign a formal ceasefire agreement by the weekend.
Fighting since war broke out in 1998 has left tens of thousands dead, and displaced hundreds of thousands of Eritreans.
Diplomats believe the current plan is sufficiently balanced to win the support of both sides - but they have warned that the process has encountered obstacles in the past, and could do so again.