Israel and Hamas appeared to be on the verge of agreeing a ceasefire deal Wednesday that would end 15 months of devastating fighting in the Gaza Strip, even as the Israel military continued to launch airstrikes in the enclave and families of Israeli hostages begged for their safe return.

American, Egyptian and Qatari delegations have been working for 15 months to secure a truce to end fighting, with officials familiar with the talks taking place in the Qatari capital of Doha saying that a…