South Sudan President Salva Kiir Maryadit gave the order on Thursday at a meeting of the government's Security Committee. Kiir is also Sudan's first Vice-President.
The armed group killed four people on Thursday in the Juba suburb of Gumbo and others the previous day along roads leading to the city.
A doctor at the Juba Teaching and Referral Hospital, who declined to be named, said: "One of the wounded brought in on Wednesday died last night", while 16 wounded were still being treated.
The South Sudan minister for internal affairs, Brig-Gen Paul Akec, told IRIN that the Security Committee had been informed on Thursday that the same group of armed men had attacked three cars on the Juba–Rejaf road.
He said the group carried out the attacks along roads from the eastern bank of the River Nile towards Juba. He said six people were killed along the Juba-Bor road; four in Juba's Gumbo suburb; seven along the Gumbo-Nesitu road; and 14 on the Nesitu–Kurangeref road.
The identity of the attackers has not been made public and Akec said: "It is not my immediate desire to talk about the identity of the attackers, no matter who they are, in order for us not to jeopardise the ongoing peace talks between the government of Uganda and the rebel Lord's Resistance Army, but we will not just sit back and watch our people being killed in cold blood."
The government of South Sudan, which is led by the Sudan People's Liberation Movement, was formed in January 2005 after the signing of a comprehensive peace agreement between the National Congress Party in the north of the country and the SPLM/Army. The agreement ended a 21-year civil war between the north-led Sudanese government and the southern-based SPLM/A.
The South Sudan government initiated the talks between the Ugandan government and LRA in mid-2006 to try to end a 20-year insurgency waged by the LRA in northern Uganda, often from bases in southern Sudan.
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