Aden has served as the headquarters of Saudi-backed former president Abd Rabbuh Mansour Hadi since he resigned some three years ago, AFP wrote.
The separatists – who want the return of the independent South Yemen that existed before 1990 – supported Hadi's forces against the Houthis but tensions between the two sides have risen in recent months.
The flare-up in Aden has added yet another dimension to one of the world's most complicated conflicts, a war that left thousands dead and millions on the brink of starvation.
On Monday, sporadic clashes continued after fighting overnight in the port city, especially in its north where separatist forces tried to take control of a military camp.
The separatists dispatched additional forces from the central province of Marib and the southern province of Abyan, security sources said.
The forces from Abyan progressed toward Aden after clashes with loyalists on the way.
On Sunday, security sources said pro-separatist units trained and backed by the UAE had taken over Hadi’s headquarters in Aden after clashes.
By early evening, separatists took control of two roads leading to the presidential palace where several members of the former government were staying, security sources said.
The International Committee of the Red Cross said fighting continued overnight in the port city.
"All night shooting in Aden #Yemen, including heavy weapons," Alexandre Faite, the head of the ICRC delegation in the country based in Sana’a, said on Twitter.
"Those in southern part of city, including (ICRC staff) still unable to get out."
UN envoy to Yemen Ismail Ould Cheikh Ahmed urged all parties to return to "calm and dialogue".
More than 13,200 people have been killed in Yemen since the Saudi-led military coalition invaded the country.
The separatists joined forces with Hadi to fight the Houthis from southern provinces in 2015, but tensions have soared since a secessionist governor's sacking last year.
Sunday's fighting in Aden killed 15 people including three civilians, hospital sources said, after separatist protesters were prevented from entering the city for a rally to demand the Hadi’s ouster.
South Yemen was independent – with former British colony Aden as its capital – from its formation in 1967 until 1990, when it was unified with North Yemen.