"The official closure of Sanaa airport, one year ago today, effectively traps millions of Yemeni people and serves to prevent the free movement of commercial and humanitarian goods", the statement signed by groups including the International Rescue Committee and the Norwegian Refugee Council said.
Citing UN figures, the NRC estimated that 7,000 Yemenis went overseas from Sanaa annually for medical treatment before the conflict.
"Without access to safe, commercial travel, Yemenis are left with no way to access critical medical care". The number exceeds the death toll of close to 9,000 people killed in violent attacks. "The only way to save my father's life was to take him overseas, the treatment needed was not available in Yemen".
NRC country director Mutasim Hamdan said it was vital that the airport reopen.
Referring to United Nations figures, the NRC estimated that before the conflict, 7,000 Yemenis went overseas for medical treatment from Sana'a every year. "Thousands of women, men and children who could have been saved lost their lives".
The Saudi-led war is aimed at reinstating the former president, Abd Rabbuh Mansur Hadi, a staunch ally of Riyadh, and undermining the country's Houthi Ansarullah movement.
The Yemeni foreign ministry said the attack was clearly meant to damage relations between the Yemeni people and Sudan and called on the worldwide community to condemn "the criminal actions" of the Houthis who control most of northern Yemen.More news: Volkswagen buys back old cars at discounts in Germany
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Since March 2015, the Saudi-led coalition of mostly Persian Gulf countries has been carrying out airstrikes against the Houthis at Hadi's request.
The country is also coping with the "world's worst cholera outbreak" as the heathcare system continues to crumble.
The Houthi media is known to regularly denounce Sudan for its participation in the Saudi-led military coalition but the group denies that any of its fighters were behind the attacks on the embassy.
It also said aid efforts have been hampered by delays and refusals of visa by the Yemeni government and by the rebels controlling the capital.
But aid groups have warned that the closure is hampering the delivery of desperately needed supplies which now have to go through the Red Sea port of Hodeida.
According to the NRC's Hamdan, "Yemen's public services are crumbling under the pressures of war".
"It is critical that all channels of domestic and global air movement are reopened so Yemenis can get help, and help can get to Yemenis", he said.