Secretary of State Antony Blinken arrived in Amman on Saturday evening ahead of expected meetings with Jordan's King Abdullah II.
The war that began on October 7 with an unprecedented attack against Israel by Gaza-based Hamas militants triggered relentless retaliatory bombardment by Israel, leaving Gazans desperately in need of humanitarian aid.
Jordan's Minister of Foreign Affairs, Ayman Safadi, in a meeting with Blinken, emphasised the "necessity of the immediate end to the aggression, of the protection of civilians in the Gaza Strip, and delivering adequate and lasting humanitarian and medical aid to all the areas of Gaza", a foreign ministry statement on X said.
Blinken, who is seeking to get more aid into besieged Gaza, visited the World Food Program's regional coordination warehouse in the Jordanian capital, live AFPTV images showed
Inside the warehouse, stocked with pallets of aid and with a beeping forklift manoeuvring, the senior UN official in Jordan, Sheri Ritsema-Anderson, described the situation in Gaza as unlike anything she had seen during 15 years in the Middle East.
It is "catastrophic. This is epic," she told reporters.
Regional tensions have soared since Tuesday when a strike in a Beirut stronghold of the Iran-backed Hezbollah movement, a Hamas ally, killed Hamas's deputy leader Saleh al-Aruri. A US Defence Department official has told AFP that Israel carried out the strike.
In brief remarks on the Greek island of Crete before he travelled to Jordan, Blinken said there is "real concern" over the Israel-Lebanon border, which even before the Aruri strike had seen daily exchanges of fire.
"We want to do everything possible to make sure that we don't see escalation there" and to avoid an "endless cycle of violence," Blinken said.
Lebanon's Hezbollah group on Saturday said it fired more than 60 rockets at an Israeli military base in retaliation for Aruri's killing.
The Israeli military said it had identified around 40 rocket launches from Lebanese territory and its forces had struck a cell responsible for firing some of them.
Additional exchanges occurred later in the day.
Blinken said he wanted to ensure that concerned countries "are also using their ties, using their influence, using their relationships with some of the actors that might be involved to keep a lid on things, to make sure that we're not seeing the spread of conflict."
Turkey has a "vital role" in that regard, said Blinken, who is making his fourth wartime trip to the region.
On Saturday Blinken met with Turkish President Recep Tayyip Erdogan and "emphasised the need to prevent the conflict from spreading," the US State Department said.
The European Union's foreign policy chief Josep Borrell carried a similar message on a visit to Beirut Saturday.
"It is imperative to avoid regional escalation in the Middle East. It is absolutely necessary to avoid Lebanon being dragged into a regional conflict," Borrell said.
From Turkey, Blinken headed to Greece where, he said, he spoke with Prime Minister Kyriakos Mitsotakis about another side-effect of the Israel-Hamas war.
Yemen's Huthi rebels have launched more than 100 drone and missile strikes towards targets in the Red Sea and Israel. This has disrupted shipping in the area vital for world trade, and contributed to the fears of wider war.
The Iran-backed Huthis say they are acting in solidarity with Palestinians.
Later Sunday, Blinken travels to the Gulf emirate of Qatar and to Abu Dhabi, capital of the United Arab Emirates.
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