"There were military clashes yesterday (Thursday) around 8 pm. Five soldiers have been killed in the incident," said Nyarji Roman, a spokesman for rebel leader turned vice president Riek Machar.
The clashes took place two days before South Sudan marks the fifth anniversary of its independence from Sudan.
Army spokesman Lul Ruai Koang told reporters that five soldiers loyal to President Salva Kiir were killed and two wounded in the shootout at a checkpoint in the city's Gudele neighbourhood.
Yesterday's violence is believed to be the first direct clashes between the army and former rebels in the capital since both took up positions there as part of the peace agreement. Gudele was the scene of tribal massacres at the outbreak of the war.
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Roman said the shooting began when two vehicles used by Machar's bodyguards were stopped by soldiers. He said two former rebels were also injured in the clash.
In other incidents, a UN worker was reportedly injured in a separate shooting and a US embassy vehicle was also shot at, Roman said.