Deng Goc, an SPLM spokesman, confirmed that the ministers were on board the aircraft and said that bad weather was to blame for the crash.
Machar gave no reason for the crash, but ruled out an attack.
"The plane had been rented from an charter company and was carrying a delegation of leaders from the Sudan People's Liberation Movement from Wau to the capital Juba," he said.
He said an inquiry would be launched.
The former rebel SPLM signed an accord with the northern National Congress Party (NCP) in 2005, ending Africa's longest civil war.
Friday's crash comes a day after southern army officials said Sudan's northern and southern forces had agreed to withdraw from an oil-rich border, where clashes killed dozens last month.
The UN said the plane was a Beachcraft 1900 operated by South Sudan Air Connection traveling from Wau to Juba.