Supplies began arriving in Yemeni ports on Monday two weeks after a Houthi missile launched at Riyadh triggered tough restrictions on goods entering the country.
A ship carrying 5,500 tonnes of flour docked in Hodeidah on the Red Sea coast - the first after the Saudi-led coalition fighting Iran-backed rebels in Yemen closed air, land and sea access to the country on November 6.
Saudi Arabia said it took the action to stop a flow of arms to the Houthis from Iran, including missile parts.
The delivery marks the first aid to arrive through Hodeidah after the coalition allowed a flight carrying aid workers to the Yemeni capital of Sanaa on Saturday.
Both Hodeidah and Sanaa are controlled by the rebels. The coalition is fighting in support of Yemeni troops loyal to the internationally-recognised government of president Abdrabu Mansur Hadi.
The coalition said it had taken the decision to allow aid through the ports after completing "a comprehensive review of the inspection and verification procedures used to implement the United Nations Security Council Resolution 2216.”
The resolution prohibits the provision of weapons and military equipment to the Houthi militia and their supporters.
Last week, the coalition eased some restrictions on ports controlled by the Yemeni government, but aid agencies had called for more to be done to allow a free flow of aid into the country.
Aid agencies said the blockade had worsened the humanitarian crisis in Yemen where the war has left an estimated 7 million people facing famine and killed more than 10,000 people.
The coalition gave clearance for UN flights in and out of Sanaa from Amman on Saturday, involving the regular rotation of aid workers.
The charity Save the Children said an estimated 20,000 Yemeni children under the age of five were joining the ranks of the severely malnourished every month, "an average of 27 children every hour".
Shortly after access as restricted, the leaders of the World Health Organisation, the UN children's agency and the World Food Programme issued a joint appeal for the further easing of restrictions at ports.
It came a day after Save the Children said an estimated 130 children or more were dying every day in Yemen from extreme hunger and disease, with more than 50,000 already believed to have died in 2017.
The UN child agency said on Sunday it has flown 1.9 million doses of vaccines to Yemen
Regional UNICEF director Geert Cappelaere described Saturday's shipment as a "very small step" at a time of immense need and warned that it must not be a one-off.
More than 11 million children in Yemen are in acute need of aid, and it is estimated that every 10 minutes a child in Yemen dies of a preventable disease, he said.
New alarms were raised by an outbreak of diphtheria, with suspected cases reported in five governorates, said Mr Cappelaere. Cholera and acute watery diarrhoea spread rapidly in recent months, including among children, with close to 1 million suspected cases reported.
"The war in Yemen is sadly a war on children," he said. "Yemen is facing the worst humanitarian crisis I have ever seen in my life."
Cappelaere said the 1.9 million doses are meant to vaccinate 600,000 children across Yemen against diphtheria, meningitis, whopping cough, pneumonia and tuberculosis.
Close to 180 cases of diphtheria have been reported in the past two months, starting from the governorate of Ibb, but spreading to four other districts.
Like other aid officials in recent months, he appealed for a swift end to the war. "The absence of a political solution to the Yemeni crisis is deplorable," he said.
