The letter accused the BBC's World Service of broadcasting information that was "downright dangerous and unprofessional".
In particular, Eritrea took issue with an "erroneous and far-fetched statement" by the BBC that "tens of thousands died in the two-and a half-year [border] war that started when Eritrean forces occupied Ethiopian administered Badme on May 1998".
The minister pointed to the April 2002 border ruling issued by an independent boundary commission which "asserts that Badme is in Eritrea" and therefore Eritrean forces could not have invaded their own territory.
The Eritrea-Ethiopian Boundary Commission recently accused Ethiopia of seeming to undermine the peace process by seeking "variations" to the delimited border line. Ethiopian officials, including Prime Minister Meles Zenawi, have recently indicated they may not accept the ruling if Badme - where the border conflict flared up - is awarded to Eritrea.
The minister's letter also took issue with the line of questioning by BBC reporter Robin White in a recent interview with Meles.
White asked the Ethiopian premier if he regretted "not having marched on Asmara or at least having taken the port of Assab when you could have done?", comments described by Ali Abdu as "equally far-fetched and off the wall".
He said it was "high time" the BBC "does its research".
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