As mediators pursue a deal that would free hostages from Gaza in exchange for a pause in Israel’s military campaign, a small group of relatives of Israeli hostages says that the government should keep waging war against Hamas — even if it prolongs their loved ones’ captivity.

Family members of three hostages say that Israel should not agree to a deal with Hamas before the Israeli military has achieved its objectives in the war. They have formed a group, called Forum Tikva, or “hope,” to press their position.

That puts them at odds with the Hostages and Missing Persons Families Forum, the main alliance of hostages’ families, which has forcefully urged Prime Minister Benjamin Netanyahu’s government to give priority to the captives’ release.

One of Forum Tikva’s founders is Tzvika Mor, whose son Eitan was working as a security guard at the Tribe of Nova music festival on Oct. 7. Eitan became one of the roughly 240 civilians and soldiers Israel says were abducted to Gaza during the Hamas-led attack that day. Any negotiation with Hamas, Mr. Mor said, should come from a position of strength.

“I want my son back now, but I want the Israeli government to make a good deal for all the people of Israel, not only for me,” he said.

His comments are a reflection of the emotionally charged debate in Israel around the fate of the hostages as the war in Gaza enters its fifth month. At least 30 of the roughly 136 remaining hostages captured Oct. 7 are believed to be dead, according to an Israeli intelligence assessment. As hostages’ families mount more aggressive protests to demand that Israel secure their release, a rift has deepened among Israelis about the cost the country is willing to absorb to have the remaining captives brought home.