Hopes rise among relatives of hostages as signs of progress in talks are reported.

Dozens of family members of Israeli hostages and their supporters gathered in protest on Thursday opposite the Israeli military’s headquarters in Tel Aviv while the country’s war cabinet convened there to discuss developments in talks aimed at securing the release of the captives.

The protesters blocked a sidewalk near the building where Israel’s top officials were meeting and, using loudspeakers, they counted to 209 — the number of days that had passed since the hostages were seized on Oct. 7. They called on Prime Minister Benjamin Netanyahu to agree to a deal that would secure the remaining hostages’ release, no matter how costly.

“Tension is very high,” said Shay Dickmann, the cousin of Carmel Gat, one of the hostages still in Gaza. “Whenever there’s talk about a deal our heart opens.”

Many of the relatives of hostages have staged similar demonstrations to Thursday’s in the months since their loved ones were taken captive. But in the last several days, they have experienced especially tense anticipation, clinging to reports indicating progress in the negotiations with Hamas.

But others in Israel — including right-wing lawmakers like Bezalel Smotrich, the country’s finance minister — have expressed disdain about the concessions the government would have to make to secure such a deal. Israel has recently said it would agree to the release of fewer hostages in exchange for a cease-fire and the release of Palestinian prisoners.

The proposal’s detractors have also raised concerns that a cease-fire would interfere with a planned ground incursion into Rafah, the southern Gaza city that Israel’s government maintains is the last stronghold of Hamas. Far-right members of Israel’s governing coalition have threatened to bring down Mr. Netanyahu’s administration if the war ends without Hamas’s total defeat.

Ms. Dickmann said she realized that the concessions Israel would have to make to reach a deal were difficult to accept but that they were “worth the lives that can still be saved.”

“I want to believe my country cares about my cousin’s life,” she said.

Opposite the protesters, in Tel Aviv’s Hostages Square, about 100 yeshiva students were studying the Torah in a new tent, a demonstration intended to promote conversations with the relatives of hostages and passers-by. The students were part of Israel’s Religious Zionist movement, whose political leaders, which include Mr. Smotrich, are generally opposed to making a deal before Hamas is completely defeated.

Their presence at the square, which has become a center of the movement calling for the government to reach a hostage-release deal, prompted lively discussion with the relatives of hostages and their supporters.

“We came here to break the ice with those on the other side,” said Amir Rochwald, a student from a yeshiva in Hebron, in the West Bank, and one of the initiative’s organizers. He added: “Even if our message is not ‘Make a deal now,’ we still want to see the hostages return.”