WASHINGTON - The US has said it is “evaluating” Hamas’ formal response to its Gaza ceasefire proposal, as the secretary of state, Antony Blinken, attempts to channel global support for a UN security council resolution backing the proposal into pressure on the Palestinian militant group and Israel.

Late on Tuesday, a Hamas official said they had submitted a response to Egyptian and Qatari mediators, seeking some “amendments”, and that their priority was to bring a “complete stop” to the war. A separate Hamas spokesperson, Jihad Taha, said the response included “amendments that confirm the ceasefire, withdrawal, reconstruction and [prisoner] exchange”.

Washington received the reply and was “evaluating it right now,” national security council spokesperson John Kirby told journalists on Tuesday night, while declining to provide details on its content.

Blinken on Wednesday heads to Qatar, which along with Egypt is a key mediator with Hamas.

On his second day of a visit to the Middle East on Tuesday, he said Israel’s prime minister, Benjamin Netanyahu, had “reaffirmed his commitment” to the proposal, although the Israeli government, which has far-right members, has not formally endorsed it.

Blinken met Israeli opposition leaders on Tuesday morning, and spoke privately to hostages’ families before travelling to Jordan for an emergency summit on humanitarian aid for Gaza, where more than a million people are on the brink of famine and most of the population are displaced.

He announced an extra $404m (£317m) funding for humanitarian aid for Gaza at the conference, and called on other countries to step up donations.

The Palestinian president, Mahmoud Abbas, said the international community had a responsibility to press Israel to open land crossings into Gaza. His Egyptian counterpart, Abdel Fattah al-Sisi, said international pressure was needed to stop Israel using hunger as a weapon.

The deal, which was approved by the UN on Monday, was unveiled by the US president, Joe Biden, at the end of May. Biden presented it as an Israeli initiative although Netanyahu has been at best ambivalent about the plan, saying any ceasefire proposal before Hamas military and governance capacity had been destroyed was a “non-starter”.

That position appears to contradict the terms of the agreement, which calls for an initial exchange of elderly, sick or female hostages for Palestinian detainees held by Israel, in the course of a first six-week halt to fighting.

The ceasefire would evolve into a permanent end to hostilities and the release of all hostages in a second phase. A final stage would see the launch of a major reconstruction effort.

Hamas’s position could also complicate progress. It has said it would only accept a permanent ceasefire deal, after one temporary break in fighting collapsed last winter, and reportedly asked for international guarantees of any ceasefire.

Senior officials from the group on Tuesday welcomed the resolution and said it was ready to negotiate details. A spokesperson, Jihad Taha, said Israel was “stalling and procrastinating and creating obstacles” so it could continue fighting.

The UN vote on Monday was the first time a deeply divided security council has endorsed a comprehensive plan for Gaza. Palestinian support for the US resolution made it much harder diplomatically for Russia or China to veto it.

The rare show of relative unity puts pressure on both parties to the conflict, though both have shown themselves to be far more influenced by local constituencies and the personal interests of leaders than by international public opinion.

Netanyahu’s government has shifted to the right since Biden unveiled the deal, with the war cabinet member Benny Gantz resigning from the government over the failure to make a long-term plan for Gaza.

That has increased the weight of hardline extremists, who want to keep fighting and have said they would resign if Netanyahu accepted a deal.

However, the prime minister is also under pressure over the fate of hostages still in Gaza, whose relatives are lobbying hard for Israel to accept the deal. They demonstrated outside Blinken’s hotel in Tel Aviv, and he also met hostages’ families.

Four hostages were rescued at the weekend by Israeli special forces, in a mission that killed more than 270 Palestinians, many of them civilians, prompting international outrage at what the top EU diplomat, Josep Borrell, called a “massacre”.

The UN human rights office said it was “shocked” by the impact on civilians of the rescue operation, and warned that Israeli forces and Hamas may both have committed war crimes.

The operation brought the total freed in military operations to just seven, a tiny proportion of the 250 people captured in the Hamas cross-border attacks on 7 October, when militants also killed about 1,200 Israelis.

Relatives say military operations cannot free all their loved ones. Most of those who are now home were handed over under a temporary ceasefire deal last November. There are still 120 held in Gaza, at least a third of whom are presumed to have died.

In Gaza there was scepticism that the deal would bring a halt to Israeli attacks that have killed more than 37,000 people, according to health authorities in the strip, and brought at least half the population to the brink of famine.

“We will believe it only when we see it,” said Shaban Abdel-Raouf, 47, displaced with his family of five to the central town of Deir al-Balah. “When they tell us to pack our belongings and prepare to go back to Gaza City, we will know it is true,” he told Reuters.

Four Israeli soldiers were killed there in an ambush on Tuesday, Israeli media reported. Forty Palestinians were killed in Gaza over the last 24 hours, and 120 injured, Gaza health authorities said.

Fears of escalating conflict between Hezbollah and Israeli forces across the northern border were also on Blinken’s agenda in Israel. Late on Monday Israeli forces killed three fighters when they hit a convoy of tankers, and on Tuesday Hezbollah fired a barrage of about 50 projectiles towards the Golan Heights.

Blinken told Gantz that the ceasefire deal for Gaza would improve Israel’s security by taming tensions on that border, the US state department said.