The White House is working on a ceasefire and hostage release agreement in Gaza, but "it's not there yet," US National Security Adviser Jake Sullivan said Sunday.

"We are working hard to try to do that. We are very engaged with key players in the region," Sullivan said, according to a transcript published by NBC.

"There is work being done to this day. There will be further talks and consultations, and we hope to be able to reach an agreement for a ceasefire and the release of the hostages, but we are not there yet," he continued.

On NBC, Sullivan also welcomed the truce agreement between Israel and Lebanon's Hezbollah that went into effect on Wednesday, calling it "a huge step forward for the Middle East," adding, "We have to protect it and make sure it is fully respected."

"Our goal is to survive these first, critical days of the ceasefire, when it is most fragile," he added.

Kuwait's Emir Sheikh Meshal Al-Ahmad Al-Jaber Al-Sabah called on Sunday for an "immediate ceasefire" in Gaza, during the opening of the 45th Gulf Summit in the Kuwaiti capital.

For his part, Israeli Foreign Minister Gideon Sa'ar said on Sunday that there were "indications" of progress that could lead to an agreement.

"What I can say is that there are indications that we may see a greater degree of flexibility on the part of Hamas due to the circumstances, including the Lebanon agreement," Sa'ar said during a press conference. He stressed that the Israeli government has "the intention to move forward on this issue."

The Israeli army announced on Saturday that it had launched several air strikes on Hezbollah sites in Lebanon.

On Wednesday, US presidential envoy Amos Hochstein said, “We strongly believe that the Lebanon agreement now opens” the door to a ceasefire in Gaza.

Hamas's attack on Israel on October 7, 2023, killed 1,207 people, according to an AFP tally based on official Israeli figures.

The Ministry of Health in Gaza announced on Sunday that the death toll from the war between Israel and the Palestinian movement, which has been ongoing for more than a year in the Gaza Strip, has exceeded 44,000.