He said the flights would increase gradually over the coming days.
Iran denies arming the Houthis and blames the conflict in Yemen on Riyadh. The coalition closed all Yemen air, land and seaports last week in response to a rebel ballistic missile attack on Riyadh.
Those ports are in Yemeni cities of Aden, Mocha and Mukalla.
The 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", the rebel-run General Authority for Civil Aviation said in a statement.
Jamie McGoldrick of the U.N. Office for the Coordination of Humanitarian Affairs said Tuesday the world body is aware of an announcement that the coalition was allowing deliveries to two ports in southern Yemen.
For the ports in rebel-controlled or disputed territories, the Saudi mission has stated that it has asked for a team of experts from the U.N.to come and discuss the ways to ensure there is no smuggling of weapons. "This will have no impact on our operations once they resume", Mr McGoldrick said.
After two years of a devastating war, the Houthis still control much of Yemen's north while the south falls under the embattled President Abd Rabbo Mansour Hadi, whose government is recognised by the worldwide community and who is supported by the Saudi-led coalition.
The Saudi-led coalition has been targeting the Houthis since they seized parts of Yemen in 2015, including the capital Sanaa, forcing President Abd-Rabbu Mansour Hadi to flee and seek help from neighboring Saudi Arabia. And amidst all this, an unrelenting blockade on airports, seaports and highways of the country by the Saudi-led coalition is only making the situation far more worse.
Some 2,000 of those deaths were the result of a cholera epidemic that swept rebel-held areas this summer, with half a million people infected.
Aden port, which is controlled by allies of Saudi Arabia, does not have the capacity, according to the United Nations, to handle the necessary volume of humanitarian cargo and would mean hazardous cross-line deliveries. And landing aid there would also involve having to cross front lines to deliver it.