"After defeating the government forces in Aden and losing the battle, the prime minister may leave Aden via an airplane to Saudi Arabia", he added.
The separatists - who had been backing the government in its war against the rebel Houthi movement - have also seized the city's military bases.
The head of the International Committee for the Red Cross mission in Yemen, Carlos Batallas, said on Twitter on Monday that the clashes in Aden had killed 36 people and wounded 185. Saudi Arabia supports Hadi's government and has led a coalition of eight Arab countries to restore him to power.
Fighters from both sides have been deployed in most areas of Aden, paralysed for the second day after 15 people were killed and dozens wounded on Sunday. With current battle lines roughly in line with the pre-1990 split between North and South Yemen, just letting the separatists take over may be the simplest path to ending the war. However, tensions between the two sides remained.
The Interior Ministry sent an urgent appeal to the Saudi-led coalition, asking for its intervention to stop attacks by the STC forces.
During the past months, government forces and the UAE armed forces operating in the southern province of Aden launched a new anti-terror offensive "to root out al-Qaida militants from their strongholds in neighbouring southern province of Abyan".
How did the clashes in Aden start?
The fighting in Aden erupted on Sunday, when a deadline issued by the separatists for the government to resign expired.
The council accused the government of "rampant corruption" resulting in a "deteriorating economic, security and social situation never before witnessed in the history of the south". Heavy clashes were reported in Dar Saad and Crater areas, with the STC reportedly taking over the 4th Presidential Guards Base in Dar Saad.
Forces loyal to the separatist Southern Transitional Council (STC) made progress against the Saudi-backed Yemeni government and seized nearly all areas in the province of Aden, a Yemeni official told Xinhua on Tuesday.