The most significant attack took place Friday when, according to the government, 182 civilians were killed in 13 kebeles, or neighborhoods. In addition, 2,000 cattle have been stolen, according to the government's communications department.
A government statement blames armed militants of South Sudan's Murle tribe for having "infiltrated" across the border between the two countries. Those targeted in the raids were from the Nuer ethnic group, which straddles the border.
It is believed the children were kidnapped to act as workers. Cross-border raids are fairly common in this region, where people battle for livestock, land and resources such as water and grazing rights.
The government expressed outrage and vowed to take action, declaring two days of mourning. Ethiopian forces are reported to have killed 60 of the attackers, the government said, but the total number of attackers is not known.
"We have to neutralize the threat, hold whoever perpetrated these heinous crimes to account," Ethiopia's communications minister, Getachew Reda, told CNN by phone from Addis Ababa, the capital.
"People have been displaced from their villages," said Reda, who returned from the region where the raids took place. "The first order of business was to try to rehabilitate them. We will put them back in their villages."
He said Ethiopia had good relations with South Sudan's government and was calling on that country to help eliminate the threat.
South Sudan is the world's newest nation, having gained independence from Sudan in 2011
following decades of civil war. But it has little infrastructure and significant poverty.
South Sudan's two major ethnic groups, the Dinka and the Nuer, have been locked in a civil war since 2013