He also stressed, during his phone call with the country's Prime Minister Maeen Abdulmalik, that "the terrorist acts committed by the Iranian-backed Houthi militia and extremist terrorist groups will not discourage the legitimate government from exercising its duties from the temporary capital of Aden".
"Dozens" more people were wounded, a medical source told AFP, although all government ministers were reported to be unharmed.
The Official Spokesman of the Coalition to Restore Legitimacy in Yemen Brigadier General Turki Al-Malki said in a statement that the "Joint Forces of the Command of the Coalition condemns and denounces the cowardly terrorist attack that took place in Aden International Airport earlier today".
At least 22 people were killed and dozens more injured in the wake of Wednesday's attack on the Aden Airport.
They are supposed to be allies in the civil war against the Houthi movement, which controls the capital Sanaa and much of north-western Yemen.
The new Yemeni government was formed following a power-sharing agreement in Riyadh earlier in December between supporters of President Hadi and the southern separatist movement which fought Hadi's forces in Aden a year ago.
"We are OK, may God protect Aden", Minister of Foreign and Expatriates Affairs Ahmed bin Mubarak said on Twitter.
Images shared on social media from the scene showed rubble and broken glass strewn about near the airport building and at least two lifeless bodies, one of them charred, lying on the ground.
In a tweet, Michael Aron, Britain's ambassador to Yemen, described "the cowardly attack on Aden Airport" as a "despicable attempt to cause carnage & chaos & bring suffering when Yemenis had chosen to move forward together". No group has yet claimed credit for the attack.
The Yemeni president officially directed the formation of a committee from the new power-sharing government to investigate the repercussions of the attack against the airport of Aden.
U.N. Yemen envoy Martin Griffiths condemned the attack in a statement: "I wish the cabinet strength in facing the hard tasks ahead".
The new government includes ministers loyal to Hadi and supporters of the secessionist Southern Transitional Council (STC), as well as other parties.
A humanitarian crisis also worsened, becoming what the United Nations now calls the most severe humanitarian catastrophe in the world. Receiving support from the United Arab Emirates, the STC was formed in 2017, two years after Saudi Arabia and other Gulf States began their intervention in the Yemen conflict.
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