The witnesses said forces loyal to the Southern Transitional Council (STC), which was formed past year to push for the revival of the former independent state of South Yemen, were apparently trying to wrest control of two bases in Aden from Prime Minister Ahmed Bin Daghr's government.
Separatist forces took over much of the city and by Tuesday evening they had surrounded the presidential palace, where the country's prime minister, Ahmed bin Dagher, and several other senior government ministers were holed up.
"The two sides in Aden are supported by countries within the Saudi-led coalition that are fighting the Houthi rebels", reports Al Jazeera.
Global charity Save the Children said it was suspending life-saving work in Aden as its staff were forced to hunker down amid gun battles that the Red Cross says have killed at least 36 people in the past three days.
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Violence reportedly erupted on Sunday after forces loyal to the STC seized the government's headquarters in the coastal city.
Events in Aden have exposed deep divisions between Hadi's government and the Saudi-UAE coalition.
In an interview with France 24's Arabic-language channel, the president of the council, Aidarous al-Zubaidi, said his fighters were still "engaged in a mission with the Saudi-led coalition".
Yemen has been locked in a devastating power struggle between internationally recognized President Hadi and Iran-allied Houthi rebels since late 2014.
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"The Transitional Council now controls the whole city of Aden practically, with the exception of the palace of Al-Maashiq [the presidential palace], which is the 'red line, '" the source said.
Soldiers stand guard as workers unload aid packages from a Saudi air force cargo plane, at an airfield Yemen's province of Marib.
Hadi went on to describe the council as "southern separatists". Southern Yemen was united with Northern Yemen in 1990.
The southern port city of Aden is considered Yemen's temporary capital and the Saudi-backed Yemeni government has based itself there since 2015.
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Almost three years on, the coalition has failed to achieve its stated aim of restoring the "legitimate" government of Hadi.