A disruption of water supplies could reverse recent gains in containing the spread of cholera, which reached about 900,000 suspected cases over the past year, he added.
Jan Egeland, a former United Nations aid chief who heads the Norwegian Refugee Council, speaking to Reuters in Geneva on Thursday, said of the blockade: "In my view this is illegal collective punishment".
An official from the rebel-run civil aviation authority confirmed that the flights had landed. The United Nations has warned that war-wracked Yemen faces a mass starvation unless aid deliveries are allowed to enter the impoverished country.
On Wednesday, the coalition said it would allow humanitarian aid into Yemen through Sana'a airport and the western port of Hodeida.
The coalition announced the closure of Yemen's air, land and sea borders on November 6, two days after a ballistic missile fired from the rebel-held territory in Yemen was intercepted over the Saudi capital, Riyadh.More news: Unions Call for ILO Convention on Gender-Based Violence
One flight evacuated five staffers of the International Committee of the Red Cross, according to Soumaya Beltifa of the ICRC in Yemen.
The UN children's fund UNICEF said Saturday's flight was carrying more than 15 tonnes, or 1.9 million doses, of vaccine for diphtheria, tetanus and other preventable diseases. The blockade intensified after Saudi authorities intercepted a long-range missile, which they said had Iranian markings, near Riyadh airport. Iran has denied supplying weapons.
In response, ships were ordered to leave the Red Sea ports of Hodeida and Salef, the only lifeline to northern Yemen where most of the population lives.
Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to fugitive former President Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
The statement described the decision to open the port of Hodeidah and Sanaa airport as a first step in addressing the humanitarian crisis in Yemen, expressing Washington's aspiration to take additional steps.
The first United Nations plane for nearly a month to bring in vaccines and other medical supplies for Yemen has landed in the rebel-held capital of Sanaa.