Machar served as the first Vice President of South Sudan under current President Salva Kiir Mayardit from 2011 until his dismissal in 2013 following a power struggle between the two leaders, Xinhua news agency reported.
The statement, which was signed by armed opposition minister of Information, Mabior Garang, did not specify which country Machar had travelled to, whose location remained unknown since July 2016.
Garang said rebel factions remained committed to the peace treaty signed with the South Sudan ruling government in August 2015.
He added that opposition groups were also in accordance with decision taken by the UN Security Council to strengthen their peacekeeping force in the country.
The decision came following a surge in violence between rival forces in the capital, which left 300 persons dead and forced thousands to flee their homes.
The South Sudanese Civil War started in December 2013 after the dismissal of Machar following an alleged coup attempt.
