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The violence happened in the state of Jonglei, a haven for armed groups.
Unmiss has been in South Sudan since the country's creation in 2011, with a remit to preserve peace and security.
Mr Akbaruddin said four Indian soldiers were also wounded in the attack, and arrangements were being made to bring those killed back to India.
The soldiers had been killed while "escorting a UN convoy", he told the AFP news agency. The UN says the attack took place between the towns of Pibor and Bor.
Correspondents say that Jonglei has been hit by widespread ethnic violence since South Sudan became independent from Sudan in July 2011 - with much of it taking place in Pibor county, where the UN peacekeeping force is based.
Unmiss chief Hilde Johnson said last month that the government was expected soon to launch an offensive against fighters loyal to local rebel leader David Yau Yau in Jonglei.
The UN has blamed Tuesday's attack on militants led by Mr Yau Yau, who South Sudan says is being armed by Sudan.
On Monday Ms Johnson urged authorities and communities in Jonglei state "to take all necessary steps to prevent inter-communal violence and attacks by armed groups which are threatening civilians and spurring a deadly cycle of violence".
"The destabilisation of Jonglei must stop," she said.
Insecurity in the state has been exacerbated by a cattle-raiding feud between rival ethnic groups, which has left hundreds of people dead and some 100,000 displaced since independence.
India is a major contributor to UN peacekeeping forces around the world and has suffered losses in the past. |