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Failure to adopt a Security Council draft resolution presented by the UAE would be "approving the war crime of denying Palestinians food, water and medicine", Jordan's Foreign Minister told Lord Cameron.
Ayman Safadi and his British counterpart held extensive talks in Amman on Wednesday. Mr Safadi posted on social media that he had stressed the importance of passing the draft resolution and the pair agreed on the need to provide sufficient humanitarian supplies to Gaza.
"I urged immediate end of the Israeli aggression on Gaza," he wrote. "Nothing justifies this brutal war. It has to stop immediately."
Lord Cameron also met King Abdullah, Queen Rania and Crown Prince Al Hussein bin Abdullah II.
The king reiterated the need for civilians to be protected and "called on the international community to pressure Israel to stop its war on the Strip", an official statement said.
He also warned disrupting basic services such as fuel, electricity and water was "unacceptable" and said Israel's aggression had exacerbated the humanitarian crisis.
Lord Cameron, who visited the Jordanian Hashemite Charitable Organisation with Prince Rashid, said the UK and Jordan were working together "to get significantly more life-saving aid to those who need it".
He described as "positive news" that a World Food Programme aid convoy from Jordan had on Wednesday reached Gaza for the first time since October 7.
He said he would continue to press for an increased flow of aid and fuel to Gaza.
The UK has refused to say how it would vote on the Security Council resolution, which has been postponed several times since Monday.
Lord Cameron, who is on his second visit to the region in his role as Foreign Secretary, will later travel to Egypt, where he is expected to meet Egyptian President Abdel Fattah El Sisi, who this week won a third six-year term in office, as well as Foreign Minister Sameh Shoukry. The Middle East tour is intended to push for a “sustainable ceasefire” and further humanitarian pauses in Gaza.
He is travelling with Britain's Minister of State for the Middle East Tariq Ahmad with the aim of progressing "efforts to secure the release of all hostages, step up aid to Gaza and end Hamas rocket attacks and threats against Israel".
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On Tuesday, Prime Minister Rishi Sunak told the Commons Liaison Committee a sustainable ceasefire is one in which Hamas is no longer able to attack Israel.
"I will be seeking to build on Israel’s decision to open the Kerem Shalom crossing to ensure significantly more aid and fuel can reach Gaza, through as many routes as possible," Lord Cameron said ahead of his return to the Middle East.
“No one wants to see this conflict go on for a moment longer than necessary. But for a ceasefire to work, it needs to be sustainable.
“If Israel is still facing Hamas in Gaza with rockets and terror tactics, not only will a ceasefire not be sustainable, a two-state solution in the longer term will also not be possible.”
In Egypt he will hear from the Egyptian Red Crescent about the effect the UK’s aid deliveries, such as wound care packs, are having in Gaza.
Lord Cameron last week announced a new batch of sanctions against leaders and financiers of Hamas, while also placing restrictions on Israelis responsible for settler violence in the occupied West Bank.
He visited Paris and Rome on Tuesday as part of UK efforts to help co-ordinate the European response to the Middle East conflict and the war in Ukraine.
