He said the flights would increase gradually over the coming days.
However other ports, including Houthi-controlled Hodeidah - where some 80 percent of Yemen's food supplies enter - will remain closed until a United Nations verification regime is reviewed to ensure no weapons reach the Houthis, the statement said.
The coalition closed all air, land and sea access to Yemen last week following the interception of a missile fired toward the Saudi capital, saying it had to stem the flow of arms to the Houthis from Iran.
The Houthi-run General Authority for Civil Aviation said in a statement the air strike "led to the total destruction of the VOR/DME radio navigation system, taking it offline and thus halting the only flights at Sanaa airport - those of the United Nations and other global organisations delivering humanitarian assistance".
It says those ports are in Aden, Mocha and Mukalla.
The United Nations Office for the Coordination of Humanitarian Affairs has repeatedly called on the Saudi regime to allow aid into Yemen, but they are often met with silence or excuses.
The United Nations has warned a total blockade could cause starvation in Yemen, where war has killed at least 10,000 people in the last two and a half years.
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A Saudi-led coalition airstrike in Yemen's capital destroyed a navigation station at Sanaa airport, which is critical to receiving already limited aid shipments, local authorities capital said on Tuesday.
"The humanitarian impact of what is happening here right now is unimaginable", Mr. McGoldrick told reporters.
He also said that the more the blockade tightens, the more the Houthis will develop their abilities to "respond to the assault of the enemy".
"The first step in this process will be taken within the next 24 hours and will include and involve the reopening of all ports and airports in areas controlled by the government of Yemen".
Saudi Arabia announced it shut down all ports after a November 4 ballistic missile attack on Riyadh near its global airport by the Shiite rebels known as Houthis.
Aden, on the south coast of Aden, is the stronghold of the internationally recognised, Saudi-backed government of President Abdrabu Mansur Hadi.
Houthi rebels in Yemen have launched fresh accusations on the Saudi-led military coalition over the bombing of Sanaa Airport which is Yemen's main worldwide airport.
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