In an interview in Istanbul, his last stop on the tour, Cameron said Israel is considering a British proposal to open its port of Ashdod to aid shipments to Gaza but that it would "take a lot of pushing" to reach an agreement.
"Achieving a pause where we stop the fighting and start looking at how to get aid in and hostages out, I think there is a prospect of that," Cameron told Reuters and a Turkish broadcaster.
"That's what I've been in the region talking about. And I think we are making some progress."
Cameron met Israeli Prime Minister Benjamin Netanyahu and other leaders during his third trip to the Middle East in just over two months. He said he pushed for a sustainable ceasefire in meetings in Israel, the Israeli-occupied West Bank where the Western-backed Palestinian Authority is based, Qatar and Turkey.
"I was pressing for what I think it is in everyone's interest, including Israel's interest: to have that immediate pause because it's only then that you can bring the hostages back home," he said.
"Israel is responsible for what happens in Gaza, and we need to avoid more of a humanitarian catastrophe."
Gaza officials said on Friday the death toll from Israel's military campaign in the Hamas-run Palestinian territory, now in its fourth month, has risen to 26,083.
The war, which began after Islamist Hamas militants killed 1,200 people and captured more than 240 hostages in a cross-border attack on Oct. 7, has displaced most of the enclave's 2.3 million people, some multiple times.
(Reporting by Jonathan Spicer; editing by Hugh Lawson and Mark Heinrich)
By Jonathan Spicer
