The United Nations said most of the airport remained intact and that it would be able to receive aid shipments once the coalition follows through on its announced loosening of the blockade of the war-torn country.
But Yemeni officials in Sanaa, which is held by the rebels known as Houthis, said the airport's runway and a ground navigation tower were damaged. Repair crews were already at work, they added, speaking on condition of anonymity as they were not authorized to talk to reporters.
Jamie McGoldrick, of the U.N. Office for the Coordination of Humanitarian Affairs, said U.N. staff had visited the airport and spoken with authorities there, and that its "runway, taxiway, ramp, terminal and air traffic control tower were not hit and are in good condition."
"This will have no impact on our operations once they resume," McGoldrick said in an email from Amman, Jordan.
The U.S.-backed coalition has been at war with the Houthis, since March 2015. The coalition closed all air, land and sea ports last week in response to a rebel ballistic missile attack on Riyadh.
The coalition said Monday that it would reopen ports in areas held by allied forces and loosen restrictions it had tightened after the firing of the missile, which was intercepted near Riyadh's international airport.
However, McGoldrick said earlier in the day that there was "no indication" the coalition was actually lifting the blockade in line with its announcement.
He said that coalition announcements of the availability of two ports in southern Yemen are "helpful," but that the key need is access to the rebel-held Red Sea ports of Salif and Hodeida, closer to large population centers.
U.N. spokesman Stephane Dujarric told reporters at U.N. headquarters in New York that without Sanaa airport and Hodeida and Salif seaports fully functioning and able to receive cargo, "the dire humanitarian situation will deteriorate further."
He said U.N. humanitarian officials are warning that "seven million people are already on the brink of famine, and the blockade will only bring them closer to it."
Dujarric said the U.N. refugee agency expressed alarm at the worsening humanitarian situation, noting that at a center for displaced Yemenis in Sanaa "hundreds more people are approaching the facility daily, saying they are no longer able to meet basic needs or afford medical care."
The agency reported that the closure of Yemen's border has halted the delivery of emergency assistance for nearly 280,000 internally displaced people, and stranded some of its staff outside the country while others lack fuel for transport, he said.
The Islamic State group meanwhile struck a fresh blow to Saudi-allied forces in the country's south, where a suicide car bombing early on Tuesday targeted security forces in the port city of Aden, killing at least six people and wounding scores.
The IS-claimed attack took place at a building in the Sheikh Othman district in the central part of the city. Residents several kilometers (miles) away heard a large explosion and saw thick black smoke rising from the area. The attack caused panic in the densely populated area, home to schools, markets and street vendors.
Ambulances rushed to the site, where the building was badly damaged, and debris and body parts littered the area.
Medical officials said six soldiers were killed, with the death toll expected to rise. The officials spoke on condition of anonymity because they weren't authorized to speak to the media.
The security building is an operations center for the Security Belt, a parallel body to the government's forces that is trained by the United Arab Emirates, a main pillar in the Saudi-led coalition that has backed Yemeni President Abed Rabbo Mansour Hadi.
Associated Press writer Jamey Keaten in Geneva contributed to this report.
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