A plane carrying 50 wounded Houthi rebel fighters has left the Yemeni capital Sana’a in a critical confidence-building measure before peace talks can get under way in Stockholm as early as Wednesday.

The evacuation on a UN-chartered plane to Muscat, Oman, represents an essential building block to the talks starting. Martin Griffiths, the UN envoy who on Monday arrived in Yemen, is trying to avoid the kind of last-minute hitch over the same issue that led to the postponement of discussions that were due to take in place in Geneva in September.

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A statement said Griffiths was “pleased to confirm 50 injured Yemenis are on their way from Sana’a to Muscat for medical treatment … and urges all Yemenis to work together in pursuit of peace and stability.”

The news was welcomed by the UK foreign secretary, Jeremy Hunt, who pointed out that he had requested Saudi agreement for the evacuation when he met the Saudi crown prince, Mohammed bin Salman, a fortnight ago.

The Yemeni conflict pits a coalition led by Saudi Arabia and the United Arab Emirates against Houthi rebels from a resistance movement formed in opposition to Saudi religious influence. Four years of war have caused a dire humanitarian situation that risks descending into widespread famine unless some way is found of allowing the free flow of humanitarian aid into the country, aid agencies and the UN have warned.

Leaders of the “Yemen quartet” – Saudi Arabia, the United Arab Emirates, the US and the UK – met in Riyadh at the weekend to discuss the continuing humanitarian crisis.

“A UN-chartered plane will arrive at Sana’a international airport Monday to evacuate 50 wounded combatants accompanied by ... three Yemeni doctors and a UN doctor, from Sana’a to Muscat,” said Turki al-Maliki, a spokesman for the Saudi-led coalition. The coalition was doing all that it could to help Griffiths’ peace efforts, he added.

Houthi rebels have said they will attend if they are guaranteed safe passage, but trust between the coalition and the Houthis is in short supply.

Previous talks planned for September in Geneva failed when the Houthi delegation did not leave Sana’a, arguing that the UN could not guarantee their safe return. They also accused the UN of failing to secure the evacuation of wounded rebels to Oman.

The last major talks were held in 2016 in Kuwait, but they broke down after 108 days of negotiations, leaving rebel delegates marooned in Oman for three months.

In recent days, Griffiths has held meetings separately with officials from both warring parties as part of efforts to lay the groundwork for talks in Sweden. In the opening round of talks, Griffiths hopes to secure a prisoner swap and a ceasefire in the strategic Red Sea port of Hodeidah as a foundation for a wider truce, including a halt to coalition airstrikes that have killed thousands of civilians and Houthi missile attacks on Saudi cities.

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The UN aid chief, Mark Lowcock, warned last week that Yemen was “on the brink of a major catastrophe”, after a trip to the war-stricken country. The UN said the conflict, and especially the recent economic crisis, were driving a big increase in severe hunger and malnutrition.

Lowcock said: “In Aden, I met emaciated children so malnourished they could barely open their eyes. Humanitarian assistance helps many of these children recover. But I also heard heartbreaking stories of children relapsing again and again because their families simply can’t afford food or proper medical care.”

He also called for an end to fighting around infrastructure critical for aid operations and commercial imports. “It is unacceptable to see men with guns inside hospitals,” he said. “Conflict and fighters must stay away from civilian facilities,” Lowcock said.

His comments came after renewed deadly clashes between Houthi rebels and pro-government forces in Hodeidah, which is a conduit for nearly 80% of the aid reaching the country.

Under heavy international pressure, including warnings of mass casualties, Saudi-backed pro-government forces have not launched a renewed all-out offensive to take the port city.

Sporadic fighting has, however, continued since a fragile truce began on November 13, and it is not always clear if Saudi-led forces have given up hope of a military victory, something that its international backers – the US and UK – insist is not achievable.

The US position is ambivalent, since elements in the Trump administration see the Yemen civil war solely through the lens of defeating Iran, the country providing most of the logistical support to the Houthi fighters.

The US Congress is due to vote again this week on whether to end US support for Saudi Arabia in the war, but the state department is trying to win back Republican support by presenting the civil war as critical to the US effort to end Iranian aggression in the Middle East.

UK-led efforts to win UN security council support for a resolution entrenching the terms of a cessation of hostilities have stalled in the past week amid hostility from Saudi Arabia, the UAE and the US. The UAE said the resolution was ill-timed and not sufficiently even-handed.