“Our soldiers have lost control of Bor to the force of Riek Machar,” said army spokesman Philip Aguer.
President Salva Kiir Mayardit has accused Riek Machar, the former vice-president, of plotting a coup – a claim he denies.
The unrest, which began in the capital Juba, has killed some 500 people and sparked fears of widespread conflict.
Since independence, several rebel groups have taken up arms and one of these is said to have been involved in the capture of Bor.
The UN has expressed concern about a possible civil war between the country’s two main ethnic groups, the Dinka of Salva Kiir and the Nuer of Riek Machar.
The organization has called for political dialogue to end the crisis, and the Ugandan government says its president has been asked by the UN to mediate between the two sides.
The UN peacekeeping mission says it is sheltering civilians in five state capitals, including Juba, Bor and Bentiu, the main town of the oil-producing state of Unity.
The US and The UK have both sent planes to airlift their nationals out of the country, and a US defense official described the situation as “getting ugly”.
Bor is the capital of Jonglei state, and even before the current unrest, it was seen as one of the most volatile areas of South Sudan.
Overnight there were reports of gun battles in the town, as renegade officers fought with troops still loyal to President Salva Kiir.
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