The UN Security Council struggled to find a unified voice Tuesday on pausing the Israel-Hamas war as aid efforts neared collapse and global economic fallout spread.

With calls growing for a new truce, Qatar-based Hamas chief Ismail Haniyeh is to visit Egypt on Wednesday for talks on a ceasefire in Gaza and a prisoner exchange with Israel, a source close to the Islamist group said.

In what they say is a show of support for Palestinians in Gaza, Yemen's Huthi rebels have repeatedly fired missiles and drones toward cargo ships in the Red Sea.

Major shipping firms have diverted their vessels as a result, pushing up oil prices, and the United States announced a new security initiative to protect the waterways vital to global trade.

US Defense Secretary Lloyd Austin on Tuesday joined a virtual meeting about the initiative set to include Britain, France, Italy, and other countries.

A top Huthi official later said any country that acts against the rebels "will have its ships targeted in the Red Sea".

Qatar, backed by Egypt and the US, helped broker a week-long truce and hostage-prisoner swap in November.

US news platform Axios on Monday reported that Mossad chief David Barnea, CIA director Bill Burns, and Qatari Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani had met in Warsaw for talks on a potential new deal.

Israel maintained its bombardment and ground combat Tuesday in the third month of the bloodiest-ever Gaza war, which started with unprecedented attacks by Hamas against Israel on 7 October.

The militants burst through the militarized Gaza border fence, killed around 1,140 people in Israel, mostly civilians, and abducted about 250, according to the latest Israeli figures.

Vowing to destroy Hamas, Israel began a relentless bombardment, alongside a ground invasion, that Hamas-run Gaza's health ministry says has killed 19,667 people.

A UN Security Council vote on a resolution calling for a ceasefire was postponed again on Tuesday, as members wrangled over wording.

Three diplomatic sources said the vote on the text, the latest version of which calls for the "suspension" of hostilities, had been pushed to Wednesday.

The United States had vetoed a previous ceasefire resolution in the council, sparking condemnation by Palestinian and humanitarian groups.

The UN estimates that 1.9 million of Gaza's 2.4 million residents are displaced.

Homes have been destroyed, forcing many into overcrowded shelters as they struggle to find cooking fuel, food, water, and medical care.

With power and communication cuts, Gazans are returning to time-worn traditions including battery-powered radio sets to get news of the war.

"Here in Gaza, we're moving backwards," said Salah Zorob, 37, outside his tent. "They're going to take us back to the Stone Age."

Tor Wennesland, the UN's special coordinator for the Middle East peace process, said delivery of humanitarian aid "continues to face insurmountable challenges".

He said Israel has taken positive "limited steps" but they fall far short of what is needed.

"Amid displacement at an unimaginable scale and active hostilities, the humanitarian response system is on the brink," he said, in the latest such warning.

Explosions were heard Tuesday night in the northern Gaza area, over a live AFPTV feed.

Strikes on Rafah overnight Monday-Tuesday killed at least 20 more people, the Hamas-controlled health ministry said, bringing more suffering to the southern town that has become a vast camp for displaced Palestinians.

In Tel Aviv, air raid sirens wailed as rockets fired from Gaza sent Israelis running into shelters before the incoming fire was intercepted by an air defense system.

Israeli army spokesman Daniel Hagari said troops were expanding operations in southern Gaza's Khan Yunis area.

"We added a full brigade and additional combat engineering forces," he said. "We must dismantle Hamas, and it will take as long as needed."

The army says 132 troops have been killed in Gaza since its ground invasion began in late October.

Hundreds of Palestinians have been detained in military operations across Gaza, and on Tuesday the army said it was investigating "the deaths of terrorists in military detention centers". It gave no details.

US officials including Austin have urged Israel to protect civilians in Gaza, a call echoed on Tuesday by British Foreign Secretary David Cameron. He urged Israel to take a "much more surgical, clinical and targeted approach" in dealing with Hamas.

A top concern for many Israelis remains the fate of the 129 hostages still held in Gaza after 80 were freed last month in exchange for 240 Palestinian prisoners.

Prime Minister Benjamin Netanyahu has faced protests from hostage relatives seeking an urgent deal to secure the captives' freedom. Meeting their families on Tuesday he said: "I will spare no effort on the subject and our duty is to bring them all back."

The Gaza war has sparked fears of regional escalation and seen Israel trade deadly cross-border fire with Iran-backed Hezbollah militants in southern Lebanon.

Four of the world's biggest shipping companies — CMA CGM Group, Hapag-Lloyd, Maersk, and MSC — have diverted their vessels from the Red Sea, as has oil firm BP, in a move that sent up energy prices.

In a statement Monday, Austin said the new maritime security initiative, Operation Prosperity Guardian, is under the umbrella of the existing Combined Maritime Forces (CMF) and led by Task Force 153.

CMF is a "coalition of the willing" whose 39 members do not have specific commitments but can assign ships, aircraft, or officers as they are able, the CMF website says.

Task Force 153, formed last year, is currently led by the US Navy with a focus on "maritime security and capacity building efforts" in the Red Sea area, according to its website.