Riek Machar also confirmed that the forces fighting the government were under his command.
South Sudan has been in turmoil since President Salva Kiir Mayardit accused Riek Machar a week ago of attempting a coup.
At least 500 people have been killed since the fighting began with the government struggling to keep control of the capital, Juba.
Riek Machar’s comments came as four US service personnel involved in evacuating US citizens were wounded when their aircraft were shot at in Bor, the capital of eastern Jonglei state.
World Christian leaders have called for a ceasefire in South Sudan, where the population is mainly animist or Christian.
The Vatican and the Archbishop of Canterbury, Justin Welby, issued a joint statement calling for the country’s weak and poor to be “spared the trauma of conflict”.
“Let us not yield to fratricidal tendencies in the name of our ethnic differences (which is what God created us to be),” they said.
Riek Machar, whose claim to control Unity could not be independently verified, said that a senior military commander, General James Koang, had gone over to the rebels earlier in the week.
However, government forces say James Koang defected alone and did not take any troops with him.
Unity, a state on the border with Sudan, produces much of South Sudan’s oil, which accounts for more than 95% of the country’s economy.
Riek Machar added that he was prepared to negotiate with the government if politicians arrested this week were released and transferred to a neutral country such as Ethiopia.
Salva Kiir also agreed to negotiations after meeting African mediators on Friday.
But government troops are currently trying to retake Bor, in one of the most volatile regions in the country.
Troops backed by helicopter gunships were advancing on the town, army spokesman Philip Aguer told AFP news agency.
A spokesman for UN peacekeepers Unmiss in Bor said considerable numbers of people had arrived over the past 24 hours from surrounding areas seeking their protection.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…