Four planes carrying life-saving aid have landed in Yemen's capital, nearly three weeks after Saudi Arabia imposed a total blockade on the Arab world's poorest country.

The aircraft - carrying urgent relief supplies, including polio and diphtheria vaccines - arrived in Sanaa on Saturday, in an attempt to ease the suffering of millions of beleaguered Yemenis and help stave off mass famine.

A Saudi-led coalition fighting Yemen's Houthi rebels closed land, sea and air access to the country on November 6. It said the move was aimed at preventing weapons from reaching the rebels.

Iran has repeatedly rejected Saudi accusations that it is giving financial and military support to the Houthis, blaming Riyadh for the protracted crisis.

Khaled al-Shaif, the director of Sanaa's international airport, said more than 40 aid flights had been cancelled since the start of the siege.

"Sanaa international airport was banned from receiving humanitarian aid aircraft for more than 19 days, that led to more than 500 UN aid workers being stuck here and the cancellation of more than forty aid flights."

Jens Laerke, spokesman for the UN's Office for the Coordination of Humanitarian Affairs (UNOCHA), said he was "encouraged by the clearance" of a humanitarian flight to Yemen, but urged the kingdom to resume commercial imports.

"We stress the critical importance of resuming commercial imports, in particular fuel supplies for our humanitarian response," he said.

"Humanitarians are serving the needs of seven million people who are completely dependent upon us."

The UN has listed Yemen as the world's number one humanitarian crisis, with 17 million people in need of food, seven million of whom are at risk of famine.

More than 2,000 Yemenis have died in a cholera outbreak now affecting nearly one million people.

Yemen's civil war has been raging since 2015, when the Houthis, a group largely composed of the Zaidi Shia minority, stormed Sanaa and deposed the internationally recognised president, Abd-Rabbu Mansour Hadi.

Since then, the Houthis, believed to be backed by Iran, have been dislodged from most of the south, but remain in control of Sanaa and much of the north.