PM Ahmed bin Daghar and members of his cabinet are believed to be holed up inside the presidential palace in Aden.
There are reports of talks between the southern separatists and government forces, who were previously allies.
The fighting opens up a new front in Yemen, splitting the alliance against Houthi rebels in the north.
It has already led to the deaths of 40 people since Sunday, the Red Cross says.
The separatists are also reported to have also seized Aden’s military bases.
Yemen’s internationally-recognised government relocated to Aden in 2015, when President Abdrabbuh Mansour Hadi and his cabinet were forced to flee the capital, Sanaa, following an offensive by the Houthis.
A assault on Sanaa prompted a Saudi-led multinational coalition to launch a military campaign to defeat the rebels. Since then, more than 9,245 people have been killed and 3 million displaced, according to the UN.
Supporters of two sides have fought alongside each other over the past three years but it has always seemed an uneasy alliance.
Before the conflict, separatist sentiment had been running high in the south, which was an independent state before unification with the North in 1990.
Although the separatists were suspicious of Mr Hadi – who is a southerner but supports continued unity with the north – they joined forces to prevent the Houthis capturing Aden and drive them out of most of the south. However, tensions between the two sides remained.
The situation was made more complex by divisions within the Saudi-led coalition. Saudi Arabia backs Mr Hadi, who is based in Riyadh, while the United Arab Emirates – a key partner in the coalition – is closely aligned with the separatists. (Courtesy BBC)