British Prime Minister Theresa May has implored Saudi leaders to ease a blockade on war-torn Yemen to "avert a humanitarian catastrophe", her office said on Thursday, echoing urgent appeals from the United Nations.

A Saudi-led coalition battling Iran-backed Huthi rebels has only partially lifted a crippling aid blockade on Yemen, which was imposed earlier this month in response to a missile fired by the Huthis that was intercepted near Riyadh airport.

May -- on a Middle East tour that took her to close ally Jordan Thursday -- met both Saudi King Salman and powerful Crown Prince Mohammed bin Salman in Riyadh late Wednesday, with the worsening crisis in Yemen topping her agenda.

"The prime minister made clear that the flow of commercial supplies on which the country (Yemen) depends must be resumed if we are to avert a humanitarian catastrophe," May's office said.

"They agreed that steps needed to be taken as a matter of urgency to address this."

Saudi Arabia is Britain's largest trading partner in the Middle East, and London has signed off on more than £3.3 billion ($4.4 billion/3.7 billion euros) worth of arms sales to Riyadh since March 2015.

That was the month that Riyadh launched its intervention against the Yemeni rebels who still control the capital Sanaa and much of the north of the country.

The war has since killed around 8,600 people, while a further 2,000 have died of cholera.

The United Nations on Monday urged the Saudi-led coalition to do "much more" to ease the blockade impeding shipments of aid and fully reopen the key rebel-held Red Sea port of Hodeida.

The coalition has allowed some supplies to reach rebel-held Sanaa and the Saleef Red Sea port, also in the Huthis' hands.

But little aid has entered through Hodeida, the main conduit for UN-supervised deliveries of food and medicine.

UN officials say Yemen could face the world's largest famine in decades unless the crippling blockade is lifted.

- 'Destabilising activity' -

During her Middle East tour, May also lashed out at Iran, Saudi Arabia's arch foe.

Sunni powerhouse Saudi Arabia and Iran, the predominant Shiite power, have a long-standing rivalry based as much in geostrategic interests as religious differences.

At a press conference in Jordan after meeting King Abdullah II, May excoriated Tehran for "destabilising activity" across the region from Yemen to Syria.

The Saudi-led coalition, which began its military intervention in Yemen in 2015, has accused Iran of supplying ballistic missiles to the rebels. Tehran denies the charge.

May called for a tougher response to Iran's "ballistic programme and proliferation of weapons" and said it was "unacceptable" for the Huthis to fire missiles at Riyadh.

Yemen's Huthi on Thursday threatened retaliation unless the blockade is lifting, implicitly threatening fresh missile attacks.

On Syria, the British premier called on all players to "unite behind" UN-led talks in Geneva and "stop creating rival" processes as Russia, Iran and Turkey push a separate initiative.

May's tour also saw her make a surprise stopover in Baghdad Wednesday where she met her Iraqi counterpart Haider al-Abadi and hailed recent military gains against the Islamic State group.

As the jihadists have lost the vast bulk of their territory in the face of multiple offensives, the West is now increasingly focusing on stopping fighters returning home to carry out attacks.

The trip to the Middle East coincided with a furore that erupted after US President Donald Trump retweeted incendiary anti-Muslim videos posted by the deputy head of a British far-right group.

May insisted in Jordan that Trump was "wrong" to post the content, despite the US leader hitting out at her after earlier criticism by suggesting she focus on defending Britain instead of react to him.