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.
The anti-government forces approached from the main gate of the Presidential Palace and tried to storm it but Saudi soldiers intervened and protected the compound, the source said on condition of anonymity.
The weekly session of the Cabinet, chaired by Custodian of the Two Holy Mosques King Salman at Al-Yamamah Palace in Riyadh, urged them to fulfill their responsibility, along with the Coalition forces, in completing the liberation of all Yemeni territories and defeating the Iranian-backed Houthi militias.
The U.S. State Department has expressed concern and called on all parties to "refrain from escalation and further bloodshed".
According to recent reports by Yemen's Health Ministry, at least 16 people have been killed in Aden and scores more injured in recent clashes between pro-government forces and southern separatists. Hadi has remained there while his government operates out of Aden.
Mr. Hadi was not in Aden when the clashes between his loyalists and the Southern Transitional Council separatists began.
Violence reportedly erupted on Sunday after forces loyal to the STC seized the government's headquarters in the coastal city.
The Saudi-led Arab Coalition to Support Legitimacy in Yemen announced that it has been watching with regret over the past two days the manner in which none of the parties has responded to the Coalition's calls for calm. "The Yemeni people are already facing a dire humanitarian crisis".
Tensions have recently started to spike between southern separatists and the government of Hadi over the control of the southern half of Yemen.
The coalition also imposed air and sea blockade to prevent weapons from reaching Houthis, who are in control of most of the northern Yemeni provinces, including the capital Sanna.
Hadi, who is based in Saudi Arabia, renewed his call for a cease-fire, saying "rebellion and weapons won't achieve peace or build a state".
In the attack in Shabwa, the militants hit a checkpoint guarded by the so-called Shabwa Elite Force, which has also been trained by the UAE, near the southern city of Ataq, the provincial capital.