The statement carried by SABA news agency controlled by anti-Houthi forces is the latest escalation between Saudi-backed forces and the Southern Transitional Council, which had been backed by the United Arab Emirates.
The whereabouts of STC leader Aidarous al-Zubaidi were not immediately known.
The STC has not commented on the decision of the anti-Houthi leadership group, known as the Presidential Leadership Council.
An earlier statement from Major General Turki al-Malki, a spokesman for a Saudi-led coalition in Yemen, said al-Zubaidi had been due to take a flight to Saudi Arabia but did not take the flight with other council officials.
"The legitimate government and the coalition received intelligence indicating that al-Zubaidi had moved a large force, including armoured vehicles, combat vehicles, heavy and light weapons, and ammunition," al-Malki said.
Al-Zubaidi "fled to an unknown location".
Saudi Arabia in recent weeks has bombed STC positions and struck what is said was a shipment of Emirati weapons.
After Saudi pressure and an ultimatum from anti-Houthi forces to withdraw from Yemen, the UAE said Saturday it had withdrawn its forces.
The tensions in Yemen have further strained ties between Saudi Arabia and the UAE, neighbours on the Arabian Peninsula that have competed over economic issues and regional politics, particularly in the Red Sea area.
Ostensibly, Saudi Arabia and the UAE have shared the coalition's professed goal of fighting against the Iranian-backed Houthi rebels, who have held Yemen's capital, Sanaa, since 2014.
