Yemeni Minister of the Local Administration Abdul Raqib Fatah had called on United Nations agencies to deliver relief and humanitarian aid to all of the country's provinces through ports and airports.
"There are more than 500 employees trapped either inside or outside being denied travel as well as 40 flights that were denied arrival at Sanaa airport", he added.
The Yemen was has killed more than 10,000 people and displaced more than 2 million, caused a cholera epidemic that had affected almost 1 million people, and drove Yemen to the verge of starvation.
The United Nations Security Council on November 9 called for the blockade to be lifted, warning that otherwise Yemen would face "the largest starvation the world has seen for decades".
The coalition had said it would lift its blockade of the port from Thursday but it remains in place.
Seven million Yemenis are completely dependent on humanitarian supplies for their survival, according to the UN.
Three other aircraft - two carrying United Nations aid workers and one carrying International Committee of the Red Cross staff - also landed at the airport, which was repaired earlier this week after a Saudi-led air strike knocked out its radio navigation systems, an AFP correspondent reported.
An official from the rebel-run civil aviation authority confirmed that the flights had landed.
McGoldrick said that a flight carrying vaccines, sufficient to begin vaccinations of about one million children, is expected to land in Sanaa over the weekend.
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. The two ports are under the control of the Houthis.
The coalition joined the Yemen war in March 2015, after the Houthis forced President Abed-Rabbo Mansour Hadi and his government to flee their temporary headquarters in the southern port city of Aden into exile in Saudi Arabia.
For more than two years, airstrikes and ground fighting have left over 10,000 people dead, driven three million from their homes and destroyed the country's already fragile infrastructure.
"Full and immediate implementation of the announced measures is a first step in ensuring that food, medicine, and fuel reach the Yemeni people and that the aid organizations on the frontlines of mitigating this humanitarian crisis are able to do their essential work", she said.