The International Committee of the Red Cross (ICRC) placed the casualty count to at least 36 killed and 185 injured.
Otherwise they will leave the battlefront and move back to Aden to assist President Hadi and the government, ' the source said.
"What a farce", Mukhtar al-Rahbi, an official in Yemen's government, said.
Fighting between southern separatists allied to the United Arab Emirates (UAE) and Saudi forces loyal to the president Hadi risk crippling their once united campaign against the Iran-aligned Houthi movement in Yemen's north.
The US State Department pressed for an end to the fighting late on Monday, calling on all parties to "refrain from escalation and further bloodshed".
The historical capital city of South Yemen, the port city of Aden, has fallen to southern separatists on Tuesday, ending just over 48 hours of fighting in and around the city, and giving the UAE-backed group de facto control over the city. But despite having a common enemy, the UAE and Hadi have been locked in a long-running power struggle, which boiled over on Sunday as clashes erupted across the government's seat of power.
Fierce fighting previously broke out between militants and the Yemeni government forces, on Sunday.
The UAE is a major component of a Saudi-led military coalition of Arab states that has supported Hadi's government since the Houthis seized much of the country, including the capital Sanaa, three years ago.
Saudi Arabia's official press agency, quoting a coalition statement, said that the coalition had been "watching with regret all over the past two days that all parties have not responded to the calls for calm" and that it had requested "all parties to speed up the cessation of all clashes immediately".
The cabinet also stressed the need to finish the liberation of all Yemeni territories, defeat Iran's Houthi militias, and avoid any reasons that may lead to division and undermining the State's institutions in Yemen. "The Yemeni people are already facing a dire humanitarian crisis".
"When the coalition launched its war in 2015 they said it was aimed at preserving a united Yemen, this is no longer the case".