They're feeling the pressure to make a deal in Jerusalem.

Calling it a "decisive moment," U.S. Secretary of State Antony Blinken conveyed how serious Washington is to end more than ten months of conflict in Gaza. 

"It is time for everyone to get to yes and to not look for any excuses to say no," he warned before meeting Israeli Prime Minister Benjamin Netanyahu on Monday, a line interpreted as an "oblique message" to Netanyahu by Israeli media, including The Times of Israel.

The tactic appears to have worked, at least, when it comes to Netanyahu. 

Blinken said after his two and a half hour meeting with the leader on Monday that Israel had accepted a proposal to bridge differences holding up a ceasefire and hostage release in Gaza, and he called on Hamas to do the same.

"In a very constructive meeting with Prime Minister Netanyahu today, he confirmed to me that Israel supports the bridging proposal," Blinken told reporters. "The next important step is for Hamas to say 'yes.' "

WATCH | What's at stake on Blinken's 9th trip to region since October: 

U.S. renews push for Middle East ceasefire

After a weekend of deadly airstrikes in the Gaza Strip, U.S. Secretary of State Antony Blinken arrived in Israel for another attempt to broker a ceasefire with Hamas.

Some Israelis push PM to end war

But it's not just Blinken pressing Netanyahu.

Israelis by the thousands have filled the streets, demanding he accept a ceasefire deal that would see Hamas release some 111 hostages from the Oct. 7 attack. Last Saturday, they marched with signs reading "stop the war" and lit fires on the streets of Tel Aviv.

Polls have found that a majority of Israelis share the view that the war should end.

Israeli officials have also urged a deal to end fighting, right up to Defence Minister Yoav Gallant, who ridiculed Netanyahu's vow to keep fighting until "absolute victory" as "gibberish." His comments were denounced by the Prime Minister's office as "anti-Israeli."

But the official line from that office seems to be shifting to "an alternate reality," noticed by commentators like Amos Harel in Haaretz newspaper.

The message from his staff and supporters? "'Deal' is no longer a dirty word and it isn't necessarily 'irresponsible'; it's something that must be seriously considered," Harel wrote in a Monday column.

Indeed, after meeting Blinken, Netanyahu's officials posted his "commitment to the current American proposal on the release of our hostages." 

WATCH | Former U.S. special enovy breaks down the complexities of ceasefire talks:

Ceasefire talks in Israel-Hamas war among most 'complex' Middle East challenges: former U.S. special envoy

David Satterfield, former U.S special envoy for Middle East humanitarian issues, says current negotiations are more complicated than any conflict he's seen in his 45 years on the file.

No agreement from Hamas leaders

Despite similar U.S. pressure, Hamas has not agreed to the new proposals, insisting that it will only release hostages if Israel pulls all its troops from Gaza and makes a commitment to end fighting for good. 

Hamas has also not attended last week's negotiations hosted by Qatari, Egyptian and U.S. mediators in Doha and is not expected to be at the table across from Israel when talks resume this week in Cairo. 

Hamas officials said last week that the group would not be taking part in the talks because it does not believe Israel has been negotiating in good faith.

Netanyahu has claimed Hamas leader Yahya Sinwar has been the main obstacle to sealing a deal.

Pressure from hard-line coalition partners

And the Israeli prime minister's current words of support for the deal may not necessarily last. 

He is also facing enormous pressure from hard-line coalition partners, like National Security Minister Itamar Ben-Gvir, who have the power to bring down Netanyahu's government.

"We must win and not go to conferences in Doha or Cairo, rather defeat [Hamas]," Ben-Gvir said last week. "Bring them to their knees."

As columnist Nahum Barnea wrote in Israel's Yediot Ahronot newspaper on Monday, "Let's face it, Netanyahu and Sinwar are not willing to pay the price for a deal." 

Despite the U.S.'s "optimistic view" for a negotiated end to the Gaza war and their diplomatic pressure, it may not be enough.