"Twelve were killed and 22 were kidnapped," government spokesman Zadig Abrha said.
While Abrha said the attack in the Gambella region near South Sudan had occurred this week, he did not specify when exactly it had taken place.
"We're in hot pursuit of the perpetrators," he said.
Abrha blamed the incursion on nomadic cattle herders from the Murle ethnic group who wanted to force children to work as labourers.
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In a similar assault in April last year, attackers from South Sudan crossed into Ethiopia, killing at least 216 people and abducting more than a hundred children, most of whom have since been freed.
South Sudan, the world's youngest nation, spiralled into war in 2013 after President Salva Kiir accused his rival Riek Machar of plotting a coup.
The ensuing fighting has killed tens of thousands of people, forced nearly 1.5 million to flee the country and disrupted agriculture so severely that the government last month declared a famine in part of the country.
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