The United Arab Emirates-backed separatists, who want to split with the north, have a rival agenda to Hadi's government over the future of Yemen.
The Saudi-led coalition intervened in Aden Sunday in support of the Yemeni government after southern UAE-backed separatists effectively took over the port city, fracturing the alliance that had been battling the Houthi movement.
The infighting, which broke out on Aug. 8 to control the port city which serves as temporary seat of Yemen's Saudi-backed has killed 40 people and injured 260, the United Nations said.
"It is heart-breaking that during Eid al-Adha (the Muslim holiday) families are mourning the death of their loved ones instead of celebrating together in peace," said Lise Grande, the U.N. Humanitarian Coordinator in Yemen.
"Our main concern right now is to dispatch medical teams to rescue the injured," she said in a statement on Sunday. "We are also very worried by reports that civilians trapped in their homes are running out of food and water."
The Saudi-led coalition, which the United Arab Emirates is one of its key members, said it attacked an area that posed a "direct threat" to the government of President Abd-Rabbu Mansour Hadi, without providing details.
In a sign of support for Yemen's beleaguered president, Saudi Arabia's King Salman met Hadi on Sunday in the Mecca region, on the sidelines of the haj pilgrimage, the state-run Saudi Press Agency reported.
A local official told Reuters the coalition had targeted separatist forces surrounding the nearly empty presidential palace in the Crater district. Hadi is based in the Saudi capital Riyadh.
Several hours after the coalition announcement, there was no indication that STC forces were preparing to leave government military camps they seized on Saturday.
STC Vice-President Hani Ali Brik, writing on Twitter to mark Eid al-Adha, that began on Sunday, said while the Council remained committed to the coalition it would "not negotiate under duress". It had earlier agreed to a truce.
The United Arab Emirates-backed separatists, who want to split with the north, have a rival agenda to Hadi's government over the future of Yemen, but have been a key part of the coalition that intervened in the Arabian Peninsula nation in 2015 against the Houthis after the group ousted Hadi from power in the capital Sanaa in late 2014.
The violence in the port city that handles some commercial imports and aid complicates U.N. efforts to end the war that has killed tens of thousands and pushed the country to the brink of famine.
Coalition member the UAE, which has armed and trained thousands of southern separatists, urged calm. Riyadh said it would host an emergency meeting aimed at restoring order. Hadi's government has asked Abu Dhabi to stop backing southern forces.
Analysts said Abu Dhabi and Riyadh, allies who see their intervention in Yemen as part of a proxy war against Iran, would work together to contain the crisis even though the UAE in June scaled down its military presence in Yemen as global pressure mounted to end the war.