At least 15 people were killed in clashes involving southern separatists, who are allied with the United Arab Emirates, and troops loyal to the Saudi-supported government in the interim capital Aden.
The sides had been united in their war against the Iran-backed Houthis who have controlled the capital in the north, Sanaa, since 2015 when they overthrew President Abd Rabbu Mansour Hadi.
What complicates matters is that the UAE is in the Saudi-led coalition fighting the Houthis.
:: What is happening in Yemen?
The fighting broke out on Sunday after a deadline set by separatists from the Southern Transitional Council (STC) for Mr Hadi to dismiss prime minister Ahmed bin Daghr's government expired.
The STC - an autonomous body not recognised by the government and aimed at overseeing self-governance in southern provinces - has accused the government of corruption and mismanagement, which it denies.
The separatists have taken control of the government headquarters in Aden and Mr Bin Daghr has denounced their actions as a "coup".
He claimed the situation was heading towards "a comprehensive military confrontation... (which is) a direct gift to the Houthis and Iran".
Armed separatists have also reportedly seized a key military base in Khor Maksar district in northern Aden and several government buildings from soldiers loyal to President Hadi.
On Monday, the secessionists, who have long demanded independence for the south, deployed more forces from the central province of Marib and southern province of Abyan.
The fighting has killed 15 people including three civilians, after separatist protesters were prevented from entering Aden for a rally on Sunday to demand the ousting of the government.
The separatists accused Mr Bin Daghr of ordering his troops to open fire on the protesters.
Former Aden governor Aidarous al Zoubeidi formed the STC last May after President Hadi fired him.
South Yemen was formed in 1967 and had former British colony Aden as its capital.
The region was independent until 1990 when it was unified with North Yemen.
More than 9,200 people have been killed in the devastating Yemen war since 2015.