There are “positive indications” that Yemen's truce may be extended, the UN said as it held talks with warring parties to the conflict.
The UN-brokered ceasefire, set to end on Thursday, began on April 2, at the start of Ramadan.
It has largely held despite allegations of breaches by the Iran-backed Houthi rebels, resulting in a nationwide calm for the first time since the six-year civil war began.
Hans Grundberg, the UN special envoy to Yemen, has been “involved in intense work on ensuring the renewal of the truce”, UN spokesman Stephane Dujarric said late on Wednesday.
Part of the truce renewal is lifting the Houthi siege on Taez province.
The Iran-backed rebels control the province's economy and are keeping civilians boxed in. Humanitarian agencies said people who needed urgent medical assistance often die on their way to Aden or Sanaa because of roadblocks.
The development comes shortly after Tim Lenderking, US special envoy for Yemen, and Steve Fagin, US ambassador to Yemen, visited Aden and met senior government officials on Wednesday.
They discussed the urgent need to extend the ceasefire and Washington's “appreciation for the government of Yemen's support for an extension of the UN negotiated truce", the State Department said.
Yemen's warring sides have held talks in Amman over the past week on lifting the siege.
However, they did not reach a deal on another provision of the agreement during three days of talks in Jordan, Mr Grundberg said on Saturday.
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The question of the blockaded city is key to extending the nationwide ceasefire.
Mr Grundberg said a proposal had been floated in what he described as “an initial round of discussions” for a phased reopening of roads in Taez and elsewhere, which would enable aid deliveries and the movement of suffering Yemenis.
He urged the government and Houthis to conclude internal deliberations and deliver “positive results to the Yemeni people” in continuing talks in Amman.
Mr Grundberg was making “intense” efforts for the renewal of the truce.
Mr Dujarric said they “received preliminary, positive indications from the parties at this point”.
Another condition is the resumption of commercial flights between the Houthi-controlled capital, Sanaa, and Jordan and Egypt.
More than a thousand passengers have flown from Sanaa to Amman and Cairo in recent weeks. Seven commercial flights have taken off from the Yemeni capital since May 16, a UN official told The National.
Wednesday's flight to Cairo was the first commercial plane to land in the Egyptian capital, making it the seventh to take off from Sanaa. The flight carried 77 Yemeni passengers and it returned from Cairo to Sanaa airport carrying 145 Yemeni passengers.
The reopening of Sanaa airport to commercial flights was part of the two-month truce. Mr Dujarric said 2,495 Yemenis had travelled between Sanaa, Amman and Cairo so far.
The US said it welcomed the resumption of commercial flights from Sanaa, a move that “enables more Yemenis to seek medical care, pursue educational opportunities and see loved ones from across Egypt’s diverse Yemeni diaspora community”.
“While we are encouraged by the resumption of flights from Sanaa and expanded flow of fuel into northern Yemen, there is much more work needed to improve the freedom of movement of people and goods inside Yemen,” said State Department spokesman Ned Price.
He said Washington was calling on Yemen's parties to “seize this pivotal moment, listen to the demands of the people, maintain support for the truce and build towards a comprehensive peace process”.
Since the ceasefire began “fighting has sharply reduced, with no aerial attacks emanating from Yemen across its borders and no confirmed air strikes inside Yemen”, Mr Grundberg said in May.
However, humanitarian needs in Yemen remain high despite improvements since the truce, with about 19 million people expected to face hunger this year, including more than 160,000 who will face famine-like conditions.
“Aid agencies need $4.28 billion to assist 17.3 million people across the country this year,” Mr Dujarric said.
However, only 26 per cent of that amount has been funded, he said, urging donors to pledge money and redeem their pledges.
The Houthi rebels seized control of Sanaa in 2014, prompting a Saudi-led military intervention to support the internationally recognised government the following year.
Hundreds of thousands of people have died in the war and the country is on the brink of famine.