At least seven critically ill people in need of medical care and their relatives have been flown out of Yemen's rebel-held capital, Sanaa, on Monday, the World Health Organization (WHO) said.

The WHO said on Twitter that the majority of the patients are women and children who suffer from conditions such as "aggressive forms of cancer and brain tumours, or who need organ transplants and reconstructive surgeries".

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The young patients flew out of Sanaa airport, which has been closed to commercial flights since 2016, aboard a UN-marked plane bound for Amman, Jordan.

"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 news agency, adding that more patients and their families would travel to Jordan and Egypt in coming days.

"It's crucially important that this first flight has gone," she said of the evacuation programme that took months to negotiate.

People board a United Nations plane that will carry them to Amman, Jordan in the first flight of a medical air bridge from Sanaa airport in Yemen [Khaled Abdullah/Reuters]

"All of us feel today that this is a major breakthrough and an indication of hope out of Yemen."

Fifteen-year-old Abdallah Abed was one of 16 patients to be flown out on the first flight to Amman.

"I have kidney failure and I need a transplant," he said. "God willing we travel today to Jordan for treatment."

Yemen has been mired in almost five years of conflict since Houthi rebels overthrew the internationally-recognised government of President Abd-Rabbu Mansour Hadi from Sanaa in late 2014. A Saudi-UAE-led military coalition intervened in 2015 to try to restore Hadi.

In November, the coalition - which controls Yemen's airspace - said patients needing medical care would be allowed to be flown out of Sanaa.

On Sunday, Houthis criticised the evacuation plan as inadequate for the needs of thousands of people in urgent need of treatment.

"The World Health Organization said it will transport via a small UN plane only seven patients with their escorts per flight," the rebels said in a statement.

"The number of people signed up for medical evacuations are around 32,000 patients with serious illnesses," the statement added.

UN Special Envoy for Yemen Martin Griffiths last month told the UN Security Council that "we are very close to seeing the first flight move 30 patients who are now waiting in Sanaa for their treatment".

"These flights will transport patients who need medical attention unavailable in Yemen to agreed locations abroad," he said.

"I really hope that by the time we meet next month ... we will have seen that first flight happen."

The Norwegian Refugee Council (NRC) welcomed the expected start of the humanitarian airlift, but said that others were handed a "death sentence" when the coalition closed the airport in Sanaa.

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

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

A WHO spokeswoman told AFP that three more flights have been scheduled for February 4, 5 and 7, bound for Amman and Cairo, Egypt.

Tens of thousands of people, mostly civilians, have been killed and millions displaced in the war in Yemen, which the UN says has caused the world's worst humanitarian crisis.