Jeremy Hunt, the UK foreign secretary, has given an upbeat assessment of the chances of political talks and a ceasefire in the four-year Yemen civil war after a visit to Riyadh ended with Saudi Arabia agreeing to allow some wounded Houthi rebels to be evacuated.

The fate of 50 injured fighters has proved the biggest single stumbling block to the start of a previous round of aborted peace talks in October, and the apparent breakthrough could pave the way for fresh negotiations, the Foreign Office said in a statement. The talks are likely to be held in Sweden.

The Foreign Office said it expected the UN special envoy Martin Griffiths to update the UN security council on Friday about his efforts to secure talks, including various confidence-building measures to be taken by both sides.

Hunt welcomed a temporary lull in the fighting in Yemen, which came after more than 150 people were killed over 24 hours as Saudi and United Arab Emirates coalition forces battled their way to the strategic Red Sea port of Hodeidah.

Facebook Twitter Pinterest Foreign secretary Jeremy Hunt with Saudi King Salman (R) in Riyadh. Photograph: Untitled/AP

Explaining the detail of the breakthrough, the Foreign Office said: “Subject to final assurances, the Saudi-led coalition [has] agreed to the evacuation of wounded Houthis from Yemen, one of the key stumbling blocks to the UN Geneva talks in September.

“Coalition forces will now permit the UN to oversee a Houthi medical evacuation, including up to 50 wounded fighters, to Oman ahead of another proposed round of peace talks in Sweden later this month.”

The Saudis blocked a similar group of 50 Houthi fighters leaving Yemen ahead of peace talks planned for Geneva last month, prompting the Houthis to refuse to attend and forcing Griffiths to abandon his efforts.

Griffiths said he welcomed reports of a slow down in the fighting in Yemen, especially around Hodeidah.

“I call upon all parties to the conflict to show continued restraint,” he said. “The people of Yemen have suffered enough. I am confident that the parties are ready to work on a political solution and am encouraged by the constructive engagement received from all sides … We are in a position to move forward.”

Griffiths said UN stood ready to re-engage the parties on a negotiated agreement for Hodeida which would protect the port and preserve the humanitarian pipeline.

During a visit to Riyadh and Abu Dhabi on Monday, Hunt met Saudi Arabia’s King Salman and Crown Prince Mohammed bin Salman, as well as leaders from the United Arab Emirates and Yemen. Afterwards Hunt said: “Diplomacy and negotiation remain the only path to ending the conflict and I am encouraged that Saudi Arabia and the UAE have shown their support for the UN peace process.”

The Foreign Office said Hunt had “constructive discussions on pathways to achieve de-escalation and reduce tensions, and was clear that both sides would need to play their part in the confidence-building measures”.

It said the UK would “continue discussions with partners on how the security council can support the UN special envoy … on the political process and improving the humanitarian situation. This will include discussions on the draft UN security council resolution on Yemen ahead of a security council briefing.” It is not clear if a resolution will be ready to be submitted as early as Friday.

The UK is the penholder on the Yemen file at the UN and has been accused of putting insufficient pressure on its close allies, the Saudis, to ensure a resolution backing a ceasefire was put to the security council. The UK claims a consensus was hard to secure given the competing national rivalries in Yemen.

But the renewed threat of famine due to an increase in violence in Yemen, the weakening of the Saudi diplomatic position in the wake of the Saudi murder of the Washington Post columnist Jamal Khashoggi and the intensity of Griffiths’ shuttle diplomacy have all conspired to make the chances of at least a start to peace talks more realistic.

The UN secretary general, Antonio Guterres, warned on Monday of a possible “catastrophic situation” if the port of Hodeidah was destroyed.

“The fighting must stop, a political debate must begin and we must prepare a massive humanitarian response to avoid the worst next year,” he said.

Hodeidah has been controlled by Houthi rebels since 2014 when they overran the capital Sana’a, then swept through most of the rest of the country.

The Saudi-led coalition intervened the following year and pro-government forces have since recaptured nearly all of the south and much of the Red Sea coast in a war of attrition, marked by gross human rights abuses by all sides, including starvation as a tactic of war.