The deadly clashes reflect deep divisions between secessionists and loyalist forces, both of whom have fought Shiite Huthi rebels.
Zubaidi said last week's violence had been "provoked" by forces loyal to Riyadh-based Yemeni President Abedrabbo Mansour Hadi. President Hadi is based in the Saudi capital Riyadh.
The force, known as the Security Belt, overran three military barracks belonging to unionist forces and were surrounding the presidential palace, sources close to the Security Belt said. "We don't know where matters are heading", Aden resident Adel Mohammed told Reuters.
A witness confirmed the complex had been handed over.
The coalition has vowed further attacks to dislodge southern fighters after hitting a separatist area on Sunday.
He called for Abu Dhabi to "immediately halt its financial and military support for those rebel groups", according to series of tweets posted on the ministry's Facebook page.
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"It is becoming increasingly obvious that the UAE and Saudi Arabia do not share the same end goals in Yemen, even though they share the same overarching goal of pushing back the perceived influence of Iran".
Separatist commanders accused the Al-Islah Islamist party of killing one of its commanders and "infiltrating" the Hadi government, which is politically and financially supported by Saudi Arabia.
Peter Salisbury, a senior analyst with the International Crisis Group, a non-profit research institute, said the situation for the Saudi-led coalition was "very fluid".
But "today's circumstances require robust diplomatic intervention from the UN, Saudi Arabia and the United Arab Emirates to avoid the worst and help forge a durable solution".
Yemeni separatists backed by the United Arab Emirates began withdrawing Sunday from positions they seized from the internationally-recognized government in the southern port city of Aden.
The Western-backed, Sunni Muslim coalition has fractured after more than four years fighting on behalf of Hadi's ousted government against the Iran-aligned Houthi movement that controls the capital Sanaa and most populous areas.
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UAE's official WAM news agency reported Saturday that the country's foreign minister, Sheikh Abdullah bin Zayed, called for an end to the military escalation in Aden.
The STC issued a statement on its website accepting the cease-fire demanded by Saudi Arabia and agreeing to enter a dialogue.
Mr Hadi's office said the two men discussed the separatist "coup" against the government and "various other crimes against the sons of Aden".
More than 70 people, including civilians, have been killed, AP news agency reported, citing Yemeni security officials.
"In less than 24 hours, Doctors Without Borders/Médecins Sans Frontières (MSF) treated 119 people in its hospital and the wounded continue to pour in", the MSF, an global medical humanitarian group, said on its official webpage on Saturday.
"Scores of civilians have been killed and wounded since August 8 when fighting broke out in the city of Aden".
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