Rocketing regional tensions are increasing the desperation of families and friends of the remaining 111 captives, including 39 known to be dead, taken during the bloody October 7 attack that sparked the Israel-Hamas war.
"We're actually very concerned and worried that there is no time," Gil Dickman, whose cousin Carmel Gat is among the captives, told AFP.
Critics say Netanyahu, who is facing a corruption trial, prefers to prolong the conflict rather than agree a deal that could upset his hardline coalition partners and tip him out of office.
Israel is now bracing for a dramatic escalation in the 10-month conflict after its killing of Hezbollah's military commander in Beirut and the death in Tehran of Hamas's political leader, which happened in quick succession last week.
Israel has not commented on the killing of Hamas chief Ismail Haniyeh, but reprisal attacks are widely expected from Iran, Lebanon's Hezbollah and other Iranian proxies in the region.
As tensions surge, anxiety is soaring among some relatives who worry that a widening war will torpedo their hopes of a deal to free the hostages.
"The hostages have no time and it seems like some people in Israel, including the prime minister, are taking their time," Dickman said.
'Ironclad' commitment
Netanyahu insists he has an "ironclad" commitment to save the hostages, with the "maximum number" of living captives to be released in the first stage of the deal it has presented to Hamas.
"I am prepared to go a long way in order to free all our hostages, while maintaining Israel's security," he said on Sunday.
Two days after the Hezbollah and Hamas killings, Netanyahu sent a negotiating team on a short-lived trip to Cairo -- a move described as "theatre" by Mairav Zonszein, senior Israel analyst for the International Crisis Group think-tank.
Qatar's prime minister, a leading figure in the negotiations mediated by Doha and Egypt, questioned whether the talks with Hamas now had any chance of success.
"How can mediation succeed when one party assassinates the negotiator on other side?" Sheikh Mohammed bin Abdulrahman Al-Thani posted on X.
Images of the hostages are ubiquitous in Israel, plastered on walls, fences and bus stops and often labelled with the hashtag #BringThemHome.
Tel Aviv's Hostages Square is a permanent monument for the captives, while Jerusalem has a smaller version with tents and banners outside Netanyahu's official residence.
Perhaps with some irony, the prime minister is not at home to see the round-the-clock vigil with its weekly marches and speeches, as the building is undergoing renovations and he is staying elsewhere.
The hostage relatives "hate him. They say that he's a fool. They think it's a catastrophe," Yael, a volunteer who did not want to give her family name, told AFP at the Jerusalem protest site.
"We feel so hopeless," she said, standing next to placards and T-shirts for the hostages.
'Did he sacrifice the hostages?'
Despite the criticism of Netanyahu, it's impossible to know his real strategy and intentions, analysts say, as the deliberations are highly secret.
"It's clear from what he says... his priority is to neutralise Hamas's military capabilities," said Emmanuel Navon, a political science professor at Tel Aviv University.
"The question is, did he sacrifice the hostages to make sure Hamas doesn't have a chance to regroup and rebuild itself? Personally, I find it hard to believe."
Palestinian political analyst Ghassan Khatib said Netanyahu would veto any deal that didn't preserve Israel's military advances in Gaza, including securing the border with Egypt, which Israel alleges was used for weapons smuggling.
"In my view Netanyahu will be OK with either a negotiated agreement that can maintain the Israeli military achievements, or no agreement," the former Palestinian minister told AFP.
"An agreement on his terms will be very difficult for Hamas to accept because that will mean the Israeli army staying in Gaza."
For Zonszein, the messaging from Netanyahu is not encouraging.
"If he was interested in both a hostage deal and preventing a regional war he would say that," she said.
"That would send a very clear signal, and he's not doing that. He's kind of doing the opposite."
Back at the vigil at Netanyahu's official residence, Yael said the protests are at least helping to sustain the hostages' relatives.
"We can't afford for them not to have hope that they (hostages) will survive," said the volunteer, wearing a sticker with "303" on her shirt, referring to their days in captivity.
"I think that is what allowed the families to survive in this really unbelievable situation."
