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Ethiopian troops were operating in South Sudan on Thursday after crossing the border to rescue about 125 Ethiopian children who were kidnapped during a bloody cattle raid, and top officials from both countries sought to coordinate their efforts.

Peter Bashir Gbandi, acting South Sudanese foreign affairs minister, said South Sudan Chief of Staff Paul Malong would go to Ethiopia's capital, Addis Ababa, as soon as Friday to coordinate. Bashir told The Associated Press that South Sudan doesn't want Ethiopian troops to go deeper into South Sudan. He said the South Sudanese army has no forces in the area but has put troops on standby.

He wouldn't answer directly if South Sudan gave permission to Ethiopia to enter but insisted, "we are in touch." He said he knew who was responsible for the attack in Ethiopia and added that the area "is full of jungle. These are criminals." Officials in both countries said there was no tension between the neighboring states.

South Sudanese local leaders, meanwhile, traded accusations over who was responsible. Ethiopia's government said the April 15 raid in its Gambela region resulted in 208 deaths. Ethiopia announced Wednesday its military entered South Sudan and surrounded the attackers, believed to be Murle tribesmen who abducted 125 children. Local media in Ethiopia reported the Murle wanted the children to raise the 2,000 head of cattle the tribal members stole.

South Sudan's Ambassador to Ethiopia, Akuei Bona Malwal, told the AP that Ethiopia and South Sudan are coordinating their actions to solve the crisis, but declined to give details about "joint tasks" which he said the two countries are carrying out.

Baba Medan, the governor of South Sudan's Boma state, where Murle and other groups live, said dissident members of the Cobra faction were responsible. The Cobra was a rebel militia comprising Murle and Anyuak tribes which signed a peace deal with South Sudan's government in 2013 and has been integrated into the national army.

David Yau Yau, who led the Cobra rebellion, denied any involvement of his former troops and accused the governor, a Murle who was allied with the government against Yau Yau during the rebellion, of arming the groups that carried out the attack in Ethiopia.

South Sudan President Salva Kiir called Ethiopian Prime Minister Hailemariam  Desalegn on Wednesday to express condolences, according to Bashir.

The U.N. children's agency, the EU and the U.S. have condemned the attack and the abductions. Residents of Gambella held a rally Thursday to demand the children's release.

It was unclear how many Ethiopian soldiers entered South Sudan or what kind of weapons they brought. The Murle, like many groups in South Sudan, are usually armed with light weapons like AK-47 assault rifles. The conflict area is a lowland with thick bush which turns swampy in the rains. It is currently the dry season, making mobility easier.

The Murle are viewed with suspicion by Dinka and Nuer, the other two dominant tribes in that area of South Sudan, and are often blamed for cattle raids and abductions of children.