Health minister Qasem Buhaibuh said the attacks had wounded 110 others, suggesting the death toll could increase further because some of the wounds were serious.
Salem Al-Shabhi, a senior health official in Aden, told The Independent the majority of those injured were in a critical condition.
Among those killed was a staff member of the International Committee of the Red Cross (ICRC), the humanitarian organisation said on Twitter. Two of its staff were unaccounted for and three were injured, it added.
An initial first explosion was caught live on air by Al-Hadath TV, which captured plumes of smoke billowing out of the terminal as the officials were disembarking form the plane.
Hundreds of panicked onlookers, security forces, and officials were then seen scrambling for safety.
It was followed by several gunshots and smaller explosions, with some media outlets reporting mortar shells and drones had hit the building.
The cabinet members, including Maeen Abdulmalik, the prime minister, were transferred safely to the city’s presidential palace.
Mr Abdulmalik tweeted: “We and the members of the government are in the temporary capital of Aden and everyone is fine.
“The cowardly terrorist act that targeted Aden airport is part of the war that is being waged against the Yemeni state and its great people.”
Hamza al-Kamaly, Yemen’s deputy minister of youth and sports, told The Independent the deputy transport minister was injured as well as other officials.
No one has claimed responsibility for the attack but Mr Al-Kamali said the authorities believed it was perpetrated by the Iran-backed Houthi rebels, who control swathes of northern Yemen and have been embroiled in a five-year war with the recognised government.
The new Yemeni foreign minister, Ahmed Awad Bin Mubarak, who was unharmed in the explosion, also accused the Houthis of being behind the attack.
“What happened will not scare us at all, it gave us more determination to move on,” he told The Independent by phone.
A senior airport security official briefly video-called The Independent from the airport where heavily armed security officers were seen taking cover while apparently looking for the perpetrators of the attack. The Independent lost contact with him.
Images shared with The Independent showed bodies, some of them charred, strewn across the ground alongside shattered glass and mangled strips of metal from the destroyed building.
Another photo showed a security officer trying to assist a man whose clothes had been torn from his body.
The attack happened as the newly formed cabinet was returning to Yemen following a deal uniting the government of President Abedrabbo Mansour Hadi with the rival southern separatists, hailing an end to one of the multiple conflicts currently devastating Yemen.
The Southern Transitional Council (STC) seeks independence for south Yemen and, despite being allied with the government against the Houthis, declared self-rule in Aden earlier this year, triggering violent clashes and complicating United Nations efforts to forge a permanent ceasefire in the overall conflict.
The reshuffle was supposed to be one step towards ending that rift.
Yemen has been devastated by a ruinous civil war that erupted when the Iran-backed Houthis swept control of the country forcing the Hadi administration to flee in 2015.
Saudi Arabia and its Gulf allies launched a bombing campaign in March that year to reinstate Mr Hadi, but five years on the fighting shows no sign of ending.
Instead it has sparked the world’s worst humanitarian crisis, with the United Nations saying 24 million people, over 80 per cent of the population, rely on aid to survive.
The World Food Programme said that by the middle of next year over 16 million people, half the population, will be facing crisis levels of food insecurity while the number of those experiencing famine-like conditions could nearly triple.
The UN special envoy for Yemen, Martin Griffiths, condemned the explosion as an “unacceptable act of violence”. He said in a tweet that it was “a tragic reminder of the importance of bringing Yemen urgently back on the path towards peace”.
Deputy minister Al-Kamali said that the government will not leave Aden and will keep working despite the attack.
“The new government was meant to be a new hope for Yemenis all over Yemen, not only for the government-controlled area,” he told The Independent.
“This is a message that the Houthis do not want stability or peace in Yemen. I can assure you we will keep working from Aden.”
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