Demonstrators gater outside of the Yeman peace talks in Stockholm, Sweden. (Photo: CGTN)

The Saudi-led coalition said it approved evacuating wounded Houthi fighters for treatment on Monday, meeting a key condition for the group to attend UN-sponsored peace talks in Sweden this week aimed at ending Yemen's nearly four-year-old war.

Prospects for convening talks have increased as Western allies press Saudi Arabia, leader of the Sunni Muslim alliance battling the Iranian-aligned Houthis, over a war that has killed more than 10,000 people and pushed Yemen to the brink of famine.

The talks could start on Wednesday, two sources familiar with the matter said, after UN special envoy Martin Griffiths shuttled between the parties to salvage a previous round that collapsed in September after the Houthis failed to show up.

The coalition agreed to a UN request to facilitate the evacuation of 50 wounded Houthis "for humanitarian considerations and as part of confidence-building measures" ahead of the talks, spokesman Turki al-Malki said in a statement.

He said a UN commercial plane would land in the Houthi-held capital Sana'a on Monday to transport them to Oman, along with three doctors.

The Houthis have said they would head to Sweden once the wounded were evacuated and if their delegation's plane was not inspected by the coalition. 

The Saudi-backed government has said it would follow the Houthis for the talks, which are also due to focus on a transitional governing body.

The alliance intervened in Yemen in 2015 to restore the internationally recognized government of Abd-Rabbu Mansour Hadi and push back the Houthis who control most population centers.

These include Sana'a and the port city of Hodeidah, now a focus of the war.

Griffiths hopes to reach a deal on reopening Sana'a airport and securing a prisoner swap and a ceasefire in Hodeidah as a foundation for negotiations for a wider truce in Yemen.