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The children left Yemen's rebel-held capital Sanaa on the first civilian flight permitted to leave in three years, The Guardian reported.

A second flight is scheduled to leave for Jordan's capital Amman on Friday, with a third scheduled for Egypt.

The Friday flight is due to evacuate 24 critically ill Yemenis from the rebel-held capital, a World Heath Organization (WHO) source said, as the UN seeks to consolidate a medical air bridge.

On the week's first flight was five-year-old Manal whose shoulder requires a simple surgery, without which her right arm has shrunk in comparison to her left. 

"I couldn't stand the sight of her," her father Abdullah Ali Lutfallah said, according to The Guardian. "It broke my heart."

Manal will be among the seven children to receive critically needed medical attention in Jordan. The petty dealings of five years of war in Yemen has prevented these so-called "mercy flights" from taking off. 

Yemen's Houthi rebels, who control most of the North, were threatening to withdraw permission up until the night before the aircraft took off, The Guardian reported. Before that, Yemen's internationally recognised government threatened to delay the process.

The Saudi-led coalition that has been fighting in support of the beleaguered Yemeni government since 2015, has kept Sanaa airport closed to commercial flights since 2016. 

But in November, the coalition announced that it was prepared to allow medical evacuations from the airport as a confidence-building measure to support UN peace efforts.

"This is the first of what we hope will be a number of flights in the medical air bridge," UN Resident Coordinator for Yemen Lise Grande told AFP after Monday's flight.

She said she hoped there would be more evacuations in the coming days, to Egypt as well as Jordan.

"It's crucially important that this first flight has gone," Grande said. "All of us feel today that this is a major breakthrough and an indication of hope out of Yemen."

The reopening of Sanaa airport is a key demand of the Houthi rebels and one of the issues being pursued by UN mediators as they seek to relaunch peace talks. 

The Houthi health ministry says 32,000 patients with serious conditions were waiting to sign up for medical evacuations.

The Norwegian Refugee Council said thousands of Yemenis had been handed a "death sentence" when the coalition closed Sanaa airport as part of an anti-Houthi blockade.

"Today's move comes too late for thousands of Yemenis who died waiting to leave the country for urgent life-saving care," said Mohamed Abdi, the NRC's country director for Yemen.

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"We hope that these medical flights will save the lives of other Yemenis. Many more are still waiting to get the healthcare they need."

The launch of the evacuations comes despite a deterioration in Yemen's conflict, with fierce renewed fighting around Sanaa despite a period of calm.

Yemen's internationally-recognised government has been fighting Iran-backed Houthi rebels since they seized control of the capital in 2014.

Tens of thousands of people, most of them civilians, have been killed and millions have been displaced in the conflict in Yemen, which the United Nations says is gripped by the world's worst humanitarian crisis.