"Today it is fair to say that Yemen is one of the worst places on earth to be a child," said Geert Cappelaere, UNICEF's regional director for the Middle East and North Africa.
"Two million children today in Yemen suffer acute malnutrition (and) almost every single Yemeni boy and girl" is in acute need of humanitarian assistance, he told a press conference in Jordan's capital Amman.
"Today we estimate that every 10 minutes a child in Yemen is dying from preventable diseases."
UN officials have warned that Yemen could face the world's largest famine in decades unless a crippling blockade by a Saudi-led coalition battling Houthi rebels is lifted.
The blockade, put in place after Saudi forces intercepted a missile fired by Houthi forces at Riyadh's international airport early this month, has further tightened the coalition's stranglehold on the rebel-held port of Hodeida, the main conduit for UN-supervised deliveries of food and medicine.
A UN plane carrying desperately needed vaccines landed in the rebel-held Yemeni capital Sanaa on Saturday after coalition forces partly lifted the blockade, after warnings that thousands of people could die.
But UN officials have said desperately needed shipments of food and medicines to Hodeida remain blocked.
Cappelaere welcomed the reopening of Sanaa airport but said much more aid was needed.
"The war in Yemen is sadly a war on children," Cappelaere said, adding that close to 5,000 children had been killed or seriously injured since the start of a Saudi-led campaign in support of the government in March 2015.
"Thousands of schools and health facilities have been damaged or completely destroyed," he said, calling for all parties in Yemen to take responsibility for the situation there.
The coalition intervened to prop up Yemen's government after the Iran-backed Houthis drove it from Sanaa.
The devastating war has since killed some 8,600 people, while a further 2,000 have died of cholera.
Yemen is highly dependent on imported wheat for its basic needs, and aid groups have warned that humanitarian deliveries cover only a small portion of what is required.
Workers unload aid shipment from a plane at the Sanaa airport, Yemen. Reuters
More than 11 million children in war-torn Yemen are in desperate need of humanitarian aid, the United Nations children's fund warned on Sunday.