EMERGENCY SUMMIT
The separatist leader, Southern Transitional Council president Aidaroos al-Zubaidi, has agreed to a proposed emergency summit in Saudi Arabia to discuss the Aden crisis.
Zubaidi said his fighters still support the coalition against the Houthis, who ousted Hadi from Sanaa in late 2014.
He did not commit to pulling forces from sites seized following clashes that killed 40 people, including civilians.
The United Nations and other groups have pulled some staff from Aden, which handles commercial and aid imports.
"We are decreasing our staff numbers in Aden until we can determine that we can safely perform all our tasks once more," U.N. spokesman Farhan Haq said in New York on Monday.
The World Food Programme has taken 17 U.N. staff and 21 others out of the city on a ship, spokesman Herve Verhoosel told Reuters in Geneva. He said six WFP staff remain in Aden.
"It is quiet now but people are still worried. We don't know where matters are heading," said Aden resident Adel Mohammed, worrying that power and water may be disrupted again.
Zubaidi said the separatists, who want an independent south Yemen, had no choice but to seize Aden following a Houthi missile strike on southern forces earlier this month.
The separatists accuse a party allied to Hadi of being complicit in that strike, which it denies.
Violence has also escalated in other parts of Yemen after the Houthis, who say their revolution is against corruption, stepped up missile and drone attacks on Saudi cities.
The coalition said it attacked Houthi targets in northern Hajjah province on Sunday that the movement said killed 11 civilians. The alliance said it was probing civilian deaths.