Questions loom over the fate of a fragile truce between Yemen’s government and Houthi rebel forces that is set to expire in a day, with aid agencies and Western governments urging warring parties to extend it.

Yemen has been gripped by war since the Iran-aligned Houthis took over the capital, Sanaa, in 2014, eventually forcing the government to flee. A Saudi-led military intervention in support of the government followed in 2015.

The deadly war has triggered the world’s worst humanitarian crisis, according to the United Nations.

A two-month truce was agreed in early April, marking a rare moment of relative calm for Yemenis. The UN has said the truce has significantly reduced the intensity of fighting in the country.

But with the truce set to expire on June 2, there are still no signs of a breakthrough in UN-backed talks between the government and the Houthis.

The Houthis have said they are considering renewing the truce. On Tuesday, however, the United States warned the negotiations were in “trouble” as it pushed for an extension to help support millions of people at risk.

Discussions on extending the truce “haven’t ended yet but seem to be in a bit of trouble”, the US ambassador to the UN, Linda Thomas-Greenfield, said.

A key issue during the negotiations has been an end to the Houthi siege of largely government-held Taiz, the country’s third-biggest city.

Despite a provision for the Houthis to open routes into Taiz being a central part of the truce agreement, it has not been implemented yet, to the anger of both the government and locals, who have held several protests demanding the siege be lifted.

Taiz has been largely cut off from the rest of government-held territory since 2015, with all supplies coming in by a single tortuous road through the mountains, and increasing journey times by several hours.

The head of Yemen’s presidential leadership council, Rashad al-Alimi, discussed the implementation of the truce with UN chief Antonio Guterres by telephone on Tuesday. He urged Guterres to “redouble the pressure on the Houthi militia to abide by its commitments to the truce, including opening roads to Taiz”, the official Saba news agency reported.

In recent weeks, the UN envoy to Yemen, Hans Grundberg, has intensified efforts to renew the truce. He tweeted on Monday that an extension was “critical to solidify benefits delivered so far and provide space to move towards a political settlement”.

His call was joined by the charity Oxfam and more than three dozen other aid groups, who stressed in a joint statement that “the gift for a better life for the people of Yemen is in your hands”.

Among the major signs that the truce was holding and effective came on May 16 when the first commercial flight in six years left Sanaa for Amman carrying 126 passengers, including critically ill hospital patients and their relatives. Since then five other flights have flown from Sanaa airport to the Jordanian capital, while a seventh left for Cairo, Egypt, on Wednesday, carrying at least 77 people, news agencies reported.

Air traffic into the rebel-held capital has been largely halted by a Saudi-led blockade since 2016, but there have been exemptions for aid flights that are a key lifeline for the population.

The truce has also seen oil tankers docking in the rebel-held port of Hodeidah, potentially easing fuel shortages in Sanaa and elsewhere.

The war in Yemen has killed more than 150,000 people and displaced millions of civilians, according to the UN.