UN Special Envoy for Yemen Martin Griffiths left Sanaa on Tuesday, wrapping up a four-day visit during which he spoke with leaders of the Shia Houthi rebel group.

Griffiths will now head to Jordanian capital Amman, a source at Sanaa’s airport told reporters on condition of anonymity due to restrictions on speaking to media.

The UN envoy arrived in Houthi-held Sanaa on Saturday to meet with leaders of the rebel group and convey conditions laid down by the United Arab Emirates (UAE) regarding the ongoing fight over Yemen’s coastal Al-Hudaydah province.

On Monday, sources close to the discussions in Sanaa told Anadolu Agency that the talks had failed to achieve any tangible breakthroughs.

According to the same sources, the Houthis have so far refused to hand Al-Hudaydah’s strategic seaport over to UN supervision, asking instead for more time to “study” Griffith’s proposals.

The battle for Al-Hudaydah entered its seventh day on Tuesday, when Yemeni government forces — backed by a Saudi-led coalition (of which the UAE is a leading member) — captured the city’s airport, according to Yemeni military sources.

Impoverished Yemen has remained wracked by violence since 2014, when Shia Houthi rebels overran much of the country, including capital Sanaa.

The conflict escalated in 2015 when Saudi Arabia and its Sunni-Arab allies — who accuse the Houthis of serving as proxies for Shia Iran — launched a massive air campaign in Yemen aimed at rolling back Houthi gains.

The following year, UN-sponsored peace talks in Kuwait failed to end the destructive conflict.

The ongoing violence has devastated Yemen’s infrastructure, including water and sanitation systems, prompting the UN to describe the situation as “one of the worst humanitarian disasters of modern times”.