US leaders have consistently warned against a ground invasion of Rafah and pressed for an alternative, more precise operation. The senior defence official described the 90-minute meeting at the Pentagon as very productive and "really quite meaty", but demurred when asked if Defense Secretary Lloyd Austin sought to condition future US military aid to Israel on an improvement of the humanitarian situation in Gaza.

Austin said the US will continue to stand up for Israel's right to defend itself in accordance with the law of armed conflict and international humanitarian law, said the official, who spoke to reporters on condition of anonymity to describe a private meeting.

The meeting, which also included Gen CQ Brown, chairman of the Joint Chiefs of Staff, comes as tensions have spiked between the US and Israel, stemming from the widespread global frustration over the escalating humanitarian crisis in Gaza and political discord surrounding efforts to achieve a ceasefire.

Israeli Defence Minister Yoav Gallant said in a statement that they discussed the "important cooperation between the Israeli and US defence establishments to ensure Israel's qualitative military edge in the region".

The US defence official said the Israeli forces should use precision targeting, which has been effective against Hamas leaders elsewhere in Gaza. The official declined to provide details about Gallant's response.

"It was a very good conversation today between the secretary and the minister. They know each other well. They trust each other. They are friends. And so the sharing of the secretary's ideas, I would say, yes, was met by very receptive ears," the official said.

At the start of the meeting, Austin said they would discuss alternative ways to target Hamas in Rafah, and he described civilian casualties in Gaza as "far too high" and aid deliveries as "far too low". But he also repeated the belief that Israel has the right to defend itself and the US would always be there to help.

Gallant, meanwhile, emphasised the ongoing threats to Israel, and said the meeting would address ways to destroy Hamas and get the Israeli hostages released, as well as plans to return displaced residents to their homes.

On Monday, Israeli Prime Minister Benjamin Netanyahu abruptly cancelled a high-level visit to Washington this week in protest over the UN Security Council decision to call for an immediate cease-fire. The US abstained, deciding not to use its veto power, and the resolution passed 14-0.

Israel says it cannot defeat Hamas without going into Rafah, where it says the group has four battalions composed of thousands of fighters. But US officials are pressing Israel to forego a ground invasion and consider other ways to defeat Hamas.

"There are ways to go about addressing the threat of Hamas, while also taking into account civilian safety. A lot of those are from lessons, our own lessons, conducting operations in urban environments," Maj Gen Pat Ryder, Pentagon press secretary, said on Monday. "I would expect the conversations to cover those kinds of things."

Israel's offensive has killed over 32,000 Palestinians, according to local health officials, and driven a third of Gaza's population to the brink of starvation. It was launched in response to Hamas' October 7 attack on Israel, which killed some 1,200 people.

Hamas-led militants also took around 250 people hostage. They are still holding around 100 hostages, and the remains of around 30 others, after most of the rest were freed during a cease-fire last year in exchange for the release of Palestinian prisoners.

The Security Council resolution calls for a cease-fire during the Muslim holy month of Ramadan. Netanyahu accused the US of "retreating" from a "principled position" by allowing the vote to pass without conditioning the cease-fire on the release of hostages.

The dispute signals an erosion in the US-Israel relationship that has been under a microscope for months as the military assault on Hamas continues, escalating the humanitarian crisis in Gaza.

White House national security spokesman John Kirby said the US was disappointed in the decision to cancel the delegation's visit this week. He said the talks with Gallant would likely include some of what the US had planned to discuss with the Israeli delegation on the possible Rafah invasion.

Gallant met Monday with Secretary of State Antony Blinken and national security advisor Jake Sullivan. Kirby said those meetings, however, had not been intended as a replacement for the delegation meetings.