A Saudi-led coalition supporting the government imposed an air and sea blockade on rebel-held territory in March 2015 and tightened it in August last year saying it was the only way to stop weapons smuggling.
But UN agencies and aid groups have called repeatedly for the airport to be reopened to allow the delivery of desperately needed relief to the millions of Yemenis caught up in the conflict who face a deadly cholera outbreak and looming famine.
The Saudi-led coalition said late Thursday that it was ready to allow the reopening of the airport on condition the UN provided support for airport security.
It said the airport remained closed "due to concerns for the safety of civilian travel and commercial flights, as well as the smuggling of weapons by the Huthis".
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In March, the coalition made a similar request for the supervision of the rebel-held Red Sea port of Hodeida but the request was rejected by the UN.
The UN has warned seven million people are on the brink of famine.