Earlier this month, the Saudi-led coalition closed access to Yemeni ports following a ballistic missile attack toward Riyadh by Houthi rebels.
Saudi Crown Prince Mohammed bin Salman accused its regional rival Iran of supplying the missile but Iranian President Hassan Rouhani denied arming the Houthis and said the attack was a "reaction" by Yemenis to coalition air strikes.
By almost every measure offered by the United Nations, the scale of the tragedy unfolding in Yemen is staggering: More than 20 million people need urgent humanitarian aid.
The UN's World Food Programme warned that current stocks of rice will run out in 111 days and wheat in 97.
"The first step in this process will be taken within 24 hours and involves reopening all the ports in areas controlled by" Yemen's internationally recognized government, which the coalition backs, read the mission's statement.
Yemenia Airlines Chief Saleh Ba Hedile said in a statement at Cairo Airport that the flights resumed following the Saudi-led coalition lifted restriction on air travel to Yemen.
Despite the Saudi announcement, a top leader of Yemen's Shiite rebels on Monday vowed retaliation against the oil-rich kingdom over its disastrous blockade of his war-torn country.
The closure of rebel-held ports was "making an already catastrophic situation far worse", they added.
But rebel-held entry points, including the crucial Red Sea port of Hodeidah, remain shut.
"The humanitarian impact of what is happening here right now is unimaginable", said the UN's aid coordinator in Yemen, Jamie McGoldrick, this week.
"And without food and safe water, the threat of starvation grows by the day".
Earlier, the heads of three United Nations agencies warned that without deliveries of vital supplies such as food and medicine "untold thousands of innocent victims, among them many children, will die".
But even before this blockade, Save the Children estimated that "50,000 malnourished children under the age of five [will] die from hunger or disease" in 2017. But the coalition has made little progress, and the rebels still control much of northern Yemen, including the capital, Sanaa. Murphy explained in the detail the agonizing death from cholera that many in Yemen have already suffered and noting that "by the end of the year there will be 1 million people diagnosed with cholera".
"To deprive this many from the basic means of survival is an unconscionable act and a violation of humanitarian principles and law", the agency directors warned.