White House spokesperson John Kirby said CIA Director William Burns was in Cairo over the weekend for a serious round of negotiations on securing the release of hostages being held in Gaza by the Palestinian militant group Hamas and Hamas was now reviewing a new proposal.

The United States hopes to forge a deal that would include a ceasefire of around six weeks in Israel's six-month-old assault to destroy Hamas in the Palestinian enclave.

Asked if there was any reason to be more optimistic about a hostage deal, Kirby told reporters: "It should be plainly obvious just by the amount of shuttle diplomacy we're doing and our counterparts are doing, we're taking this very, very seriously. And we really want to come to closure on a hostage deal as soon as possible."

Hamas killed 1,200 people in its rampage into southern Israel on Oct. 7, according to Israeli tallies. More than 33,000 Palestinians have been killed in Israel's response, the health ministry in Hamas-ruled Gaza said on Monday. Israel's army says more than 600 of its soldiers have been killed in combat.

Kirby said Washington wanted to see a sustained pace of 300 to 350 aid trucks entering Gaza every day, and a better safeguarding of aid workers' safety after last week's Israeli airstrikes killed seven World Central Kitchen staff. "Obviously we need to see this number increase, and we need to see it sustained to really address the dire humanitarian situation," he said.

He said Washington was still reviewing the conclusions of the Israeli military investigation into the incident.

Australian Prime Minister Anthony Albanese said on Monday that Israel had yet to provide an adequate explanation for the deaths of the aid workers, including an Australian citizen and a dual U.S.-Canadian national. Two Israeli officers have been dismissed and others reprimanded.

Kirby said U.S. officials hoped to meet next week for delayed discussions with senior Israeli officials on plans by Israel for a ground invasion on Rafah in southern Gaza. He said Washington did not see a Rafah invasion as imminent and Israel had assured U.S. officials it would not proceed before taking part in talks on alternatives.

U.S. national security adviser Jake Sullivan would meet Israeli opposition leader Yair Lapid this week during Lapid's visit to Washington, Kirby said without providing details.

(Reporting by Andrea Shalal and Doina Chiacu; Editing by Howard Goller)

By Andrea Shalal and Doina Chiacu