Each side blames the other for starting the two-day battle which broke out on Sunday, saying also that their rival suffered the most losses.
There was no immediate response from Ethiopia, which has not released numbers killed.
"More than 200 TPLF (Ethiopian) troops have been killed and more than 300 wounded," Eritrea's Ministry of Information said in a statement, calling it a "conservative estimate".
There was no mention of any prisoners of war.
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Eritrea won independence from Ethiopia in 1991 after three decades of war, but returned to battle in 1998-2000, when nearly 80,000 died.
The neighbours are bitter enemies, with tens of thousands of troops dug into trenches eyeing each other along the heavily fortified frontier.
Open-ended, compulsory national service makes Eritrea one of the world's most militarised nations, but with just five million citizens it is dwarfed by Ethiopia, Africa's second most populous nation with some 96 million people.
UN Secretary-General Ban Ki-moon yesterday urged both governments to exercise "maximum restraint," and resolve differences through peaceful means. The United States has voiced similar "grave" concerns.
Eritrea and Ethiopia have long traded accusations of attacks and of backing rebels to needle each other.
Barnes said that one theory for the clash was that it was a "response by Addis Ababa to an armed action by the Asmara-linked Ginbot 7 group in southern Ethiopia in May", referring to an outlawed opposition force.
The two countries remain at odds over the flashpoint town of Badme, awarded to Eritrea by a United Nations-backed boundary commission but still controlled by Ethiopia.