There was no immediate comment on the incident from Eritrean authorities.
Meles Zenawi, the Ethiopian prime minister, has accused some of the opposition candidates of having links with Eritrea and local armed groups allegedly supported by Asmara.
Authorities have blamed Eritrea of organising past attacks in the capital by arming the separatist Oromo Liberation Front and the Ogaden National Liberation Front, while Asmara has accused Ethiopia of supporting armed groups in its country.
About 80,000 people died in a border conflict between the two neighbours in 1998-2000, many in brutal first world war-style trench warfare.
A UN-backed boundary commission charged with demarcating the border handed the disputed town of Badme to Eritrea but Ethiopia has so far refused to implement the ruling.