Benjamin Netanyahu has described his three-hour meeting with Antony Blinken as “positive” and says it was “conducted in good spirit”, with pressure for a ceasefire growing.
The US Secretary of State is making his ninth trip to the region since Israel’s war on Hamas began in October.
The US expressed optimism about a ceasefire deal after talks resumed in Doha last week.
However, Hamas has said suggestions of progress are an “illusion”, with a number of issues between the two sides still contested – including whether Israeli troops will be required to withdraw fully from Gaza.
Earlier that day Mr Blinken also met with Israel’s President Isaac Herzog and said it was “probably the best, maybe the last opportunity” to secure a ceasefire and hostage release deal in Gaza.
“We’re working to make sure that there is no escalation, that there are no provocations, that there are no actions that in any way could move us away from getting this deal over the line, or, for that matter, escalating the conflict to other places, and to greater intensity,” Mr Blinken said during his meeting with Mr Herzog.
He said it was “probably the best, maybe the last opportunity” to get the hostages released and achieve a ceasefire.
A statement from Mr Netanyahu’s office following his talks with Mr Biden said: “The prime minister reiterated Israel’s commitment to the latest American proposal regarding the release of our hostages – taking into account Israel’s security needs, which he insists on firmly.”
The current negotiations are based on a modified proposal presented by the US, aimed at bridging long-standing gaps between Israel and Hamas.
The Americans hope they can get the deal over the finish line perhaps as soon as this time next week.
But that level of optimism is not shared by the Israeli leadership or Hamas.
Each accuses the other of obstinate cynicism, and blocking a deal.
In a statement on Sunday, Hamas accused Israeli Prime Minister Benjamin Netanyahu of putting “obstacles” in the way of an agreement and “setting new conditions and demands” with the aim of “prolonging the war”.
It added it holds him “fully responsible” for thwarting mediators’ efforts and “obstructing an agreement”.
A Hamas source earlier told Saudi media that the proposals include the IDF maintaining a reduced presence along the Philadelphi Corridor, a narrow strip of land along Gaza’s southern border with Egypt.
But Israeli sources have told the Times of Israel, external that other procedures along the border could compensate for an Israeli withdrawal from the area in the first phase of the deal.
The Israeli military launched a campaign in Gaza to destroy Hamas in response to an unprecedented attack on southern Israel on 7 October, during which about 1,200 people were killed and 251 taken hostage.
More than 40,000 people have been killed in Gaza since then, according to the territory’s Hamas-run health ministry.
A ceasefire deal agreed in November saw Hamas release 105 of the hostages in return for a week-long ceasefire and the freeing of some 240 Palestinian prisoners in Israeli jails. Israel says 111 hostages are still being held, 39 of whom are presumed dead.
Earlier this week, US President Joe Biden said “we are closer than we have ever been” to a deal.
But previous optimism expressed during months of on-off talks has proven unfounded.
Mr Netanyahu told a cabinet meeting on Sunday that complex negotiations were taking place to secure the return of hostages, but some principles needed to be upheld for Israel’s security.
“There are things we can be flexible about, and there are things we cannot be flexible about, and we insist on them. We know very well how to differentiate between the two,” he said.
He also accused Hamas of being “obstinate” in negotiations and called for further pressure to be applied on the militant group.
A senior Hamas official told the BBC on Saturday: “What we have received from the mediators is very disappointing. There has been no progress.”
It is possible the public statements of defiance are mainly a negotiating tactic – but there is such significant enmity and distrust here that a week feels very optimistic for a breakthrough.
And the US pressure also has the timing of Washington’s electoral politics in the background. It feels like the countdown clock for a deal is ticking that bit faster for the Americans than it has been for the two sides in this conflict.
The original deal outlined by President Biden, based on Israel’s 27 May proposal, was to run in three phases:
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The first would include a “full and complete ceasefire” lasting six weeks, the withdrawal of Israeli forces from all populated areas of Gaza, and the exchange of some of the hostages – including women, the elderly and the sick or wounded – for Palestinian prisoners held in Israel.
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The second phase would involve the release of all other living hostages and a “permanent end to hostilities”.
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The third would see the start of a major reconstruction plan for Gaza and the return of dead hostages’ remains.
Meanwhile, the Hamas-run health authority in Gaza says Israeli air strikes killed at least 21 people including six children on Sunday.
The IDF said on Sunday it had destroyed rocket launchers used to hit Israel from the southern Gaza city of Khan Younis, the scene of intense fighting in recent weeks, and killed 20 Palestinians.
