Washington DC - The White House is working on a ceasefire and hostage release deal in Gaza but is "not there yet," the US National Security Advisor told NBC on Sunday, with fighting in the conflict raging on as Arab leaders meet in Cairo to discuss the crisis.

"We are working actively to try to make it happen. We are engaged deeply with the key players in the region, and there is activity even today," said Jake Sullivan, according to a transcript released by the broadcaster.

"There will be further conversations and consultations, and our hope is that we can generate a ceasefire and hostage deal, but we're not there yet," he added.

Sullivan's comments came a day after Israel hit Hezbollah targets in Lebanon, days into a fragile ceasefire in its conflict with the Iran-backed group.

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Addressing that conflict, Sullivan lauded the ceasefire deal and said the US was working with Lebanon's military to ensure it was implemented "effectively."

"We need to protect it and ensure that it is fully implemented," he told NBC.

Speaking in Jerusalem on Sunday, Israeli Foreign Minister Gideon Saar said there were "indications" progress could be made on a deal securing the release of hostages by Hamas in Gaza.

"There are signs we may see a greater degree of flexibility from Hamas as a result of circumstances that have developed, including the agreement with Lebanon," he said.

"There is a desire to move forward on this. I hope it can progress. We are committed to the return of the hostages – it's a responsibility we must uphold."

Saar asserted, however, that Hamas "cannot be allowed" to continue to rule Gaza.

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Hamas seized 251 hostages during its October 7, 2023, attack on Israel, with 97 still being held in Gaza, including 34 who have been confirmed to be dead.

The armed group's attack resulted in 1,207 deaths, mostly civilians, according to an AFP tally of Israeli official figures.

Israel's subsequent assault on Gaza, which has slaughtered at least 44,429 people, has been classified as a genocide.

The US has continued to fund the assault with billions of dollars worth of deadly weapons despite international outcry over Israel's conduct in the war.

Much of Gaza has been reduced to rubble, with its population dependent on humanitarian aid that the UN on Sunday said it would pause delivery of through the key Kerem Shalom crossing due to security concerns.