"It is critical that this truce," which was renewed in June for another two months "can also deliver on easing the suffering of the people of Taez," said envoy Hans Grundberg, noting that for years, Yemenis' "freedom of movement has been greatly impeded by this conflict."

Despite a UN proposal for an agreement to gradually reopen roads and ensure the safety of civilians using them, particularly on the important route between Taez and the Hawban region, nothing has yet come of the idea.

"While I am encouraged by the positive response by the government of Yemen to the UN proposal, I am still waiting for a response" from the Huthis, the Swedish diplomat said.

Grundberg said that after "constructive discussions" with the Huthis in the capital Sanaa last week, "I urge [them] to respond positively without delay to the UN proposal."

"The truce offers a rare opportunity to pivot towards peace that should not be lost," he said.

Surrounded by mountains, Taez, which has around 600,000 inhabitants, has been almost cut off from the outside world since 2015.

The truce in effect since April 2 has led to a reduction in fighting and in civilian casualties, as well as the resumption of commercial flights from Sanaa and better humanitarian access in the country.

Yemen, one of the poorest countries in the world, has been devastated by almost eight years of war between the Iran-backed Houthi rebels and government forces supported since 2015 by a coalition led by neighboring Saudi Arabia.