The White House’s envoy, Steve Witkoff, is in Qatar to join indirect talks between Israel and Hamas on extending the fragile ceasefire in Gaza.

This week, negotiators from both sides have begun meeting mediators for the first time since President Donald Trump took office on 20 January. The 42-day first phase of the Gaza deal and temporary truce came into effect on the eve of his inauguration.

That first phase ultimately saw Hamas return 25 living Israeli hostages and the remains of eight others – in exchange for about 1,800 Palestinian prisoners held by Israel – as well as five living Thai hostages. It ended on 1 March.

Israel now hopes the US can advance a plan for a two-month truce extension, which would start with the release of about half of the living hostages still held.

Hamas has so far rejected that, demanding immediate talks on the second phase in the original ceasefire agreement, which would end the war and lead to a full Israeli troop withdrawal.

However, it stated that it was approaching the ongoing discussions in Doha with “full responsibility and positivity”.

Since the start of this month, Israel has blocked all aid deliveries – including food and fuel – to Gaza, saying it aims to put pressure on Hamas.

Electricity has also been cut to the only desalination plant in the territory providing clean water, so that it is now running at a reduced capacity on generators using fuel reserves.

In response, the Houthi movement in Yemen said on Tuesday that it would restart attacks on Israeli ships passing through the Red Sea and Gulf of Aden, threatening to throw a key maritime route into chaos once again.

There is growing alarm at the potential impact of Israel blocking goods to Gaza, with some of its allies warning that this could violate international law.

The local UN Humanitarian Co-ordinator, Muhannad Hadi, has stated: “Any further delays [on aid entering] will further reverse any progress we have managed to achieve during the ceasefire.”

“We pray that these matters get resolved urgently,” a baker, Husam Rustom, told the BBC.

With the halt to supplies of flour and cooking gas, he said his bakery – which had been providing over 2,000 packs of bread a day – had been forced to close as well as several others in the southern city of Khan Younis.

“We are exhausted and tired of all this. It’s driving us mad,” said Zeinab al-Bayuk, a grandmother. She added that food prices had been rising rapidly.

Mariam Abu Mukhimer, a student, opposed an extension of the existing truce. “There needs to be a solution that ends the war,” she said. “It’s enough!”

The US has never confirmed it, but Israel’s Prime Minister Benjamin Netanyahu said on 2 March that Witkoff had proposed a temporary extension of the ceasefire until after the Islamic holy month of Ramadan and the Jewish holiday of Passover.

According to this plan, which Netanyahu said Israel had accepted, half of the hostages would be released together at the outset, and the other half at the end.

The PM suggested Witkoff had “even defined his proposal as a corridor for negotiations on the second stage. Israel is ready for this.”

It is believed that Hamas is still holding up to 24 living hostages in Gaza and the remains of 35 others. An American-Israeli soldier, 21-year-old Edan Alexander, is among those said to be alive. There are also the bodies of four other American citizens.

Hamas has accused Israel of reneging on the original ceasefire deal.

Despite pressure from regional mediators – Qatar and Egypt – as well as the US, it is thought unlikely that the armed group will give up many of the hostages without a full end to fighting in Gaza. It sees them as its major bargaining chips in talks.

For the relatives and supporters of Israelis held captive, these are desperate times.

Since Saturday, some have been camping outside the defence ministry in Tel Aviv to demand an immediate Gaza ceasefire deal that would free everyone in captivity.

“How can I start processing our personal tragedy when the national trauma is not yet over?” said Ofri Bibas, the sister of Yarden Bibas, at the protest on Monday evening.

The recent exchanges with Hamas led to the release of her brother and the return of the bodies of her sister-in-law, Shiri, and two young nephews, Ariel and Kfir, who were killed in Gaza.

“I have 59 brothers and sisters who are in hell,” Ofri continued – referring to the total remaining number of hostages. “We received Yarden alive, but Shiri and the children could have been saved. By Passover, everyone must be home, and the only way to bring everyone back is to end the war. Now.”

A poll for Israel’s Channel 13 TV indicates that half of Israelis believe that the US president is more concerned about the fate of the hostages than Netanyahu.

Asked which of the two they thought was more concerned, 50% of respondents said Trump, 29% Netanyahu, and the rest were not sure.

Far-right allies of the prime minister have threatened to collapse his governing coalition if fighting does not resume in Gaza to achieve its war goal of crushing Hamas.

Up to now, both Israel and Hamas have largely refrained from returning to all-out hostilities in the Palestinian territory.

However, recently, Israel has carried out daily strikes. On Tuesday, four men were killed in Wadi Gaza, which is also known as the Netzarim Corridor – an area from which Israeli forces withdrew as part of the Gaza ceasefire terms.

The Israeli military said its air force had targeted “several terrorists engaged in suspicious activity posing a threat to [Israeli] troops”.

Speaking to the BBC in Gaza City, the father of one of those killed, Arafat Hana, said his son, Omar, had done nothing wrong.

He said he was with neighbours walking to a displaced people’s camp where they had previously stayed to retrieve belongings.

“They were innocent. They were just going to get mattresses and other things. They weren’t carrying rockets!” said Umm Tareq Obaid, who lived near the men.

The new threats from the Houthis have the potential to end a period of relative calm in the wider region which began with the Gaza ceasefire on 19 January.

Over 15 months from November 2023, they used missiles and drones to attack more than 100 merchant ships, saying they were acting in solidarity with Palestinians in Gaza. Many vessels had no connection to Israel. Two sank, one was seized, and four sailors were killed.

The Houthis say they now want “to pressure the Israeli usurper entity to reopen the crossings to the Gaza Strip and allow the entry of aid, including food and medical supplies”.

However, there has been no immediate sign of ships being targeted.

The attacks led by Hamas on 7 October 2023 killed more than 1,200 people in southern Israel, mostly civilians, with 251 taken hostage. Most women and children held captive were released during a week-long truce in November 2023.

The unprecedented, deadly assault triggered a war in Gaza that has since killed more than 48,500 people, most of them civilians, according to figures from the Hamas-run health ministry which are used by the UN and others.