The United States is still working with mediators Egypt and Qatar to present a revised proposal for a ceasefire in the war in Gaza, State Department spokesperson Matthew Miller said.
Mr Miller told reporters he does not have a timetable for the proposal, which has been expected for several weeks, but said Washington wanted to make sure it is a proposal that can get Israel and Hamas to an ultimate agreement.
Israeli opposition leader Yair Lapid called for Prime Minister Benjamin Netanyahu to seal a truce deal immediately, as he met top US officials in Washington.
"I believe that any political interests should be set aside for this. This is way more important," Mr Lapid told reporters outside the State Department after meeting Secretary of State Antony Blinken.
"Israel as a nation will not heal unless we will bring them back home," Mr Lapid said of the hostages. "This is essential to our existence."
"It's doable," he said. "We can do a hostage deal -- and we need to do it."
Mr Lapid, a former prime minister, renewed his promise not to work to topple Mr Netanyahu's government - which relies on support from far-right members - if he goes ahead with the deal.
While describing Hamas as a "terrible terrorist organisation," Mr Lapid said that Mr Netanyahu's government "should do more" to reach a deal to free hostages.
On 31 May, US President Joe Biden put forward a plan for a ceasefire in the bloody Gaza war that would include a six-month freeze in fighting and a release of captives.
Mr Blinken has previously insisted that Mr Netanyahu was on board with US proposals to bridge gaps and complete the deal, which enjoys wide support from the Israeli public.
Mr Netanyahu has publicly rejected US assessments that the deal is nearly complete and has insisted on an Israeli military presence on the Egypt-Gaza border, angering Cairo.
Hamas ready for 'long war'
The push for a new deal comes as Hamas chief Yahya Sinwar said the Palestinian group had the resources to sustain its fight against Israel, with support from Iran-backed regional allies, nearly a year into the Gaza war.
Mr Sinwar, who last month replaced slain Hamas leader Ismail Haniyeh, said in a letter to the group's Yemeni allies that "we have prepared ourselves to fight a long war of attrition".
Deadly fighting raged on in the besieged Gaza Strip, where medics and rescuers said that Israeli strikes - which the military has not commented on - killed at least two dozen people.
The latest strikes came as Israeli Defence Minister Yoav Gallant warned that prospects for a halt in fighting with Hezbollah militants in Lebanon were dimming, yet again raising fears of a wider regional conflagration.
Senior Hamas official Osama Hamdan told AFP at the weekend the group "has a high ability to continue" fighting despite losses, noting "the recruitment of new generations" to replace killed militants.
Mr Gallant last week said Hamas, whose 7 October attack triggered the war, "no longer exists" as a military formation in Gaza.
Mr Sinwar, in his letter to Yemen's Huthis, threatened that Iran-aligned groups in Gaza and elsewhere in the region including Lebanon and Iraq would "break the enemy's political will" after more than 11 months of war.
"Our combined efforts with you" and with groups in Lebanon and Iraq "will break this enemy and inflict defeat on it," he said.
Independent UN rights experts meanwhile warned that Israel risked international isolation over its actions in Gaza and called on Western countries to ensure accountability.
Spain, which recently joined several European countries in formally recognising the State of Palestine, is due to host Palestinian president Mahmud Abbas tomorrow, an official in his office told AFP.
Mr Abbas, who is based in the Israeli-occupied West Bank and holds little sway in Gaza, is set to meet Spanish King Felipe VI and Prime Minister Pedro Sanchez, before heading to New York for the UN General Assembly.
