The UN’s special envoy for Yemen, Martin Griffiths, is accompanying a Houthi negotiating team to Stockholm for the first peace talks on the war in the country since 2016, amid fears that one misstep could cause the fragile summit to collapse.

Negotiators from the Saudi-backed government of President Abd Rabbu Mansour Hadi are expected to follow the Houthis to Sweden in time for talks to begin as early as Wednesday.

An initial focus of the discussions will be confidence-building measures, including how to implement a massive prisoner-swap programme agreed in principle and to be overseen by the International Committee of the Red Cross (ICRC).

The parties will also discuss the potential future UN administration of Hodeidah, the strategic port through which most aid travels. The talks are taking place against a backdrop of continued fighting.

Iranian-backed Houthi fighters seized control of the capital, Sana’a, in March 2015 in protest at rising oil prices, ousting the UN recognised Hadi government. Supported militarily by Saudi Arabia and the United Arab Emirates, the Hadi government has been fighting to win back control of the country, leading to mass famine and tens of thousands of civilian deaths.

Griffiths is trying to learn the lessons of the previous failed talks in September, when Houthi negotiators felt unable to travel to Geneva after undertakings about wounded soldiers and the return of the negotiators to Yemen at the end of the talks were not met.

Partly by staying physically close to the Houthis, Griffiths appears to have made more progress with the often divided group than any previous UN mediator.

The Houthi team and Griffiths left on a plane chartered by Kuwait, one of the Middle East’s mediator countries, on Tuesday.

The Hadi government’s team will follow the Houthis, reversing the choreography of Geneva where Hadi’s team was left waiting for the Houthis to arrive.

In the first step of a tortuous process the Hadi government on Monday allowed 50 Houthi fighters to fly to Oman for treatment accompanied by doctors.

The UK foreign secretary, Jeremy Hunt, said the transfer of the wounded fighters was “the essential precondition for the talks”.

The deal on prisoner swaps would cover between 1,500 and 2,000 members of the pro-government forces and between 1,000 and 1,500 rebels, according to a government official, Hadi Haig.

The ICRC will identify the individuals to be released, and the modalities of the release.

Pressure was also being applied on Hadi’s government to pay the salaries of civil servants in Houthi-controlled areas, and to allow the opening of the international airport at Sana’a.

Hadi himself has been an exiled leader, often in Riyadh and recently in the US. He is not held in high regard by the Emiratis, and the government delegation will be led by the Yemeni foreign minister, Khaled Alyemany.

The Yemeni government has increasingly relied on Washington’s belief that Iranians have been using Yemen as a base to attack Saudi Arabia, but US senators are putting unexpectedly strong pressure on the Trump administration to end US support for the war.

David Miliband, the president of the International Rescue Committee humanitarian organisation, and one of the international figures watching the Yemen crisis most closely, urged the US to keep pressure on Saudi Arabia to negotiate.

“We call on the US and UK, as military supporters to the Saudi- and Emirati-led coalition in Yemen, to use their influence to encourage meaningful dialogue in these talks and ensure the result is a reduction in violence, improved humanitarian and commercial access around the country… and salary payments to public sector workers,” he said.

Anwar Gargash, the United Arab Emirates foreign affairs minister, said the Sweden talks were a “critical opportunity” to find a political resolution. “A sustainable Yemeni-led political solution offers the best chance to ending the current crisis. A stable state, important for the region, cannot coexist with unlawful militias,” he said.

The UN humanitarian chief, Martin Lowcock, freshly back from Yemen, said the country will need billions next year and predicted the talks would not be a fast process.

Hunt has also disclosed UK plans to hold a vote on a new UN resolution calling for a ceasefire in Yemen have been delayed until after the peace talks have concluded.

Pressed by the shadow foreign secretary, Emily Thornberry, Hunt conceded the UK had to make compromises on the draft text of the UN resolution. “I can confirm both the original text, and the current text, refers to international humanitarian law, but in the process of getting that text agreed, did we make compromises to the Saudis, did we make compromises to the Houthis? Yes, we did, and as a result of this diplomacy, talks are happening this week.”