The White House insisted that the “ball was in Hamas’s court” on whether to accept a new Gaza peace proposal, despite mixed signals from Benjamin Netanyahu reflecting turmoil within his governing coalition in Israel.

The US national security spokesperson, John Kirby, insisted on Monday that it was an Israeli proposal – despite the fact it had been unveiled by Joe Biden on Friday, during the Jewish Sabbath, and Netanyahu had appeared to challenge it. The Israeli prime minister said any deal that did not lead to the complete destruction of Hamas’s military and governing capacity would be a “non-starter”.

The Israeli prime minister told the Knesset on Monday: “The claims that we have agreed to a ceasefire without our conditions being met are incorrect.”

“I’ve heard different statements coming out of Israel,” Kirby said, pointing out that the country’s foreign minister, Israel Katz, had acknowledged that it was an Israeli proposal. The three-phase plan outlined by Biden on Friday, he added, “accurately reflects that proposal, that we worked with the Israelis on”.

“Hamas has now got this proposal. It got it Thursday night. We’re awaiting an official response by them,” Kirby said. “They ought to take the deal. This gives them what they’ve been looking for, which is a ceasefire and over time, through phases, the potential withdrawal of Israeli forces from Gaza.”

“It is fair to say that the ball is in Hamas’s court,” he said.

US officials said that the proposal had evolved in discussions between US, Israeli and Qatari negotiators in the past few weeks. However, Netanyahu was given just a few hours’ notice on Friday that Biden would make it public.

The officials said that the timing, with Biden speaking when Israeli government offices were closed for the Sabbath and the country’s most conservative, religiously observant politicians had cut themselves off from the internet and other communications, was not deliberate, but was dictated by the fact that the four and a half page plan was delivered to Hamas on Thursday.

It was transmitted to the Hamas political leadership based in Qatar but officials said it could take time for it to be conveyed to Yahya Sinwar, the group’s leader in Gaza, and for a reply to come back from him.

The first phase of the proposal would be similar to an earlier plan that failed to win agreement. Over six weeks, Hamas would release elderly, sick, wounded and female hostages, and Israel would free a greater number of Palestinian detainees. There would be a ceasefire and Israeli forces would pull back from densely populated areas, allowing Palestinians to go back to whatever is left of their homes, and 600 trucks of humanitarian assistance would cross into the coastal strip each day.

At the same time there would be negotiations on how to reach a second, more comprehensive, phase, which would involve the release of all remaining hostages and the freeing of more Palestinian prisoners, a complete withdrawal of Israeli troops and a permanent cessation of hostilities. A third phase would address reconstruction and governance in Gaza.

One of the innovations of the new proposal is a clause saying the initial six-week ceasefire would extend as long as negotiations for a second phase continued, so there would not be a looming deadline that would trigger a return to combat.

It is in the transition between the first and second phase where the gaps between Biden and Netanyahu’s versions are the greatest. The plan, as spelled out by the US president, suggested that Hamas and Israel would negotiate the second phase, but the Israeli prime minister insisted that Hamas would have to be smashed before there could be an enduring ceasefire.

Biden said that Hamas was no longer in a position to launch another attack like its 7 October attack on southern Israel, which killed 1,200 people and triggered the current Gaza war, implying that Israel had achieved its military objections, but Netanyahu suggested to the obliteration of the extremist group had to be more extensive and final.

A spokesperson for the Israel Defense Forces (IDF), Rear Adm Daniel Hagari, said on Monday evening that the military would be able to ensure Israel’s security in any Gaza truce and hostage release deal decided on by the government.

The IDF also said that four more of the Israeli hostages held by Hamas have died in captivity and their bodies are being held by the Islamist group. The four dead hostages were named as Haim Perry, Yoram Metzger, Amiram Cooper and Nadav Popplewell, all of whom had appeared alive in hostage videos posted earlier by Hamas. About 120 hostages are still unaccounted for in the wake of the 7 October attack, of whom 40 are thought to have died in the course of the war.

Netanyahu told his cabinet on Monday that Israel’s first priority in Gaza is to destroy Hamas, and the first stage of the plan announced by Biden on Friday could be implemented on its own without agreeing to an end to the war.

“This is not something that I am adding now. This is not something that I am adding because I am under pressure within the coalition. It is something we agreed on unanimously in the war cabinet,” Netanyahu said in a video statement.

US officials admitted that part of the reason Biden unveiled the peace proposal was to lock in the Israeli war cabinet to acknowledge its terms and its ownership of the plan, conscious that Netanyahu was reluctant to go public with something that could wreck his government.

Since Friday, Netanyahu has come under intense pressure from the rightwing of his government. Itamar Ben-Gvir, the national security minister, accused the prime minister of trying to whitewash the peace deal, and restated his threat to quit the government if Israel entered a deal that did not specify the total destruction of Hamas as a military and political force.

The finance minister, Bezalel Smotrich, has also threatened to resign over the deal, arguing Israel’s only option was to increase military pressure on Hamas.

“The dangerous proposal that President Biden spoke of was made by the war cabinet without authority and against the law, and it is not binding for the government of Israel and state of Israel,” Smotrich said.

Israel’s Kan Radio reported that the prime minister had “promised his political partners that the war would not end and said that he believed that the chances of reaching a deal were very low”.