Regional UNICEF director Geert Cappelaere described yesterday's shipment as a "very small step" at a time of immense need and warned that it must not be a one-off.
The coalition had promised to reopen Yemen's main airport in the capital of Sanaa and the Red Sea port of Hodeida to humanitarian traffic by late last week.
However, two UNICEF vessels carrying food, water purification tables and medicines heading to Hodeida have not yet received clearance to dock, Cappelaere said.
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.
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New alarms were raised by an outbreak of diphtheria, which has already spread to five governorates, he told reporters in the Jordanian capital of Amman. Close to 1 million people in Yemen, including many children, suffer from cholera or acute watery diarrhea.
"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."
The Saudi-led coalition tightened its Yemen blockade on November 6, in response to rebel missile fire toward the Saudi capital.
Since then, the coalition has come under growing international pressure to ease the restrictions.
Last week, it said it would reopen Sanaa airport and the port of Hodeida to humanitarian aid shipments by the end of that week.
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.
The delivery of vaccines yesterday "cannot be a one-off," he said, adding that many more supplies, including vaccines, are needed.
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.
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