TEL AVIV—Renewed fighting between Israel and Hamas is sparking heightened concern among families of the roughly 140 Israelis still held captive—the majority of them men—after the end of a weeklong truce.

The pause in fighting had led to the release of dozens of hostages, most of them women and children. Many families hoped Israel and Hamas could strike a similar deal to release men, but the militant group regards fighting-age men as soldiers and the hostages it still holds as valuable leverage.