JUBA, Sept 25 (Reuters) - South Sudan's army is moving its forces out of the country's capital, in accordance with a peace agreement signed with rebel forces aimed at ending a conflict that erupted in December 2013, an army commander said.

Under the peace agreement signed by President Salva Kiir and rebel leader Riek Machar in August, the capital, Juba, and some other centres will be demilitarised.

Shifting the army, the SPLA, out of Juba marks a step towards implementing the agreement, although both sides have been accused by international mediators of violating a permanent ceasefire that was put in place after the pact was signed.

Major General Marial Chanuong Yol Mangok, who is commander of Kiir's presidential guard, told reporters on Thursday that the redeployment of the army outside Juba had started. The shift will be completed when the army establishes camps for the troops in other parts of the country.

"We are going to make a report to the SPLA general headquarter to direct our engineering team to start digging water and putting in place some of infrastructure such that people will live in," he said.

When Kiir signed the agreement, more than a week after Machar, he cited reservations about aspects, including the demilitarisation of Juba.

The conflict erupted after a long-running political row between Kiir, president since independence in 2011, and March, who was sacked as his deputy. More than 2 million people have fled their homes and thousands have been killed.

The peace agreement includes a power-sharing arrangement, under which Kiir will stay on as president and Machar is expected to become first vice president, putting the two men back into the same government again. (Reporting by Denis Dumo; Writing by Edmund Blair; Editing by Larry King)