The Saudi-led Arab coalition said on Thursday that the situation in Aden was stable following three days of clashes and that all parties were committed to defeating the Iran-backed Houthi rebels.
The coalition statement, carried by state news agency Wam, came after it sent a high-ranking military delegation to Aden to assess the response to its call for a ceasefire in the country's interim capital.
Violence broke out on Sunday after supporters of the Southern Transitional Council, a secessionist body which is battling Houthi rebels alongside government forces, called for the Yemeni cabinet to resign. Fighting between the council's supporters and government troops left dozens of combatants dead.
The coalition said Saudi and Emirati generals met both sides to realign their focus on the battle against the Iran-backed rebels as the militants' control of the capital, Sanaa, begins to falter.
Both members of the Arab Coalition are committed to supporting Yemeni forces and urge the country to maintain its focus, the statement said.
Coalition delegates emphasised the need for the ceasefire to go on so that residents of Aden could resume daily life.
"Our goal is to insure the security and stability in Aden and to end all the arguments between the rivals," a member of the delegation, Saudi Major General Mohammed Saeed Al Mugheidi said in a televised statement.
The delegation held meetings with both sides in Aden to address their grievances and resolved several of the concerns that led to the violence, a source told The National.
Yemenia Airways, the country's flag carrier, resumed operations from Aden's international airport on Thursday with flights between the southern port city and Cairo, the airline said in a statement carried by the official Yemen News Agency.
Flights to and from Aden were cancelled on Monday and Tuesday because of the clashes.
The internationally recognised government of President Abdrabu Mansur Hadi was forced to move to Aden after the Houthis seized the capital in September 2014.
The rebels later advanced south, prompting the coalition to intervene in the war. Since then, the coalition has helped pro-government forces to recapture much of Southern Yemen from the Houthis, although they still control parts of the north.
The delegation's visit to Aden came as the United States argued in the UN that fragments from missiles recovered in Saudi Arabia after being fired from Yemen by the Houthis bear marks proving they were Iranian-made. Some security analysts have questioned whether the evidence is watertight.
Vassily Nebenzia, Russian ambassador to the UN, said it was unclear whether missile parts that Security Council members were taken to see in Washington on Monday were Iranian or that a violation of a 2015 arms embargo on Yemen had taken place.
Russia was the only country to abstain from UN Resolution 2216, which demanded an end to violence in Yemen and for the Houthis to "withdraw from all areas seized”.
"Yemen hosts a pile of weapons from the old days," Mr Nebenzia said, with "many countries competing to supply weapons to Yemen during the time of [former president Ali Abullah] Saleh. So I cannot give you anything conclusive. I am not an expert to judge."
Coalition spokesman Colonel Turki Al Maliki on Wednesday said social media reports that Houthis controlling Sanaa had launched a ballistic missile targeting King Khalid International Airport in Riyadh were "untrue".
''However, a failed attempt by Iran-backed Houthi militias to launch a ballistic missile that ended in an uninhabited desert was detected,'' he said.
Col Al Maliki said the Houthis had admitted through their media operations that they targeted civilians and civilian facilities in violation of international humanitarian law.