“He is a pillar and the symbol of the military and jihadi work, and he is among the decision makers,” said Fawzi Barhoum, a Hamas official in Gaza. Without specifying whether Mr. Deif was alive or dead, Mr. Barhoum said Mr. Deif, his wife and son “are part of the body that has the resistance as its soul.”

Prime Minister Benjamin Netanyahu of Israel refused to respond specifically to questions about Mr. Deif at a news conference in Tel Aviv on Wednesday. Mr. Netanyahu said only: “The heads of terror organizations and their commanders are a legitimate and top priority target. Nobody is immune.”

Ronen Bergman, an Israeli journalist specializing in security affairs who is researching a book on Israel’s intelligence and counterterrorism efforts, said: “Deif is the only prime military figure in Hamas to have survived so long. The fact that he was able to escape multiple assassination attempts and recover from severe injuries has built him the image and prestige of a bulletproof legend.”

Whether Mr. Deif was eliminated or not, the targeting of one of his family shelters is likely to roil the Hamas leadership and raise internal fears of a security leak.

At a news conference in Gaza on Wednesday, the masked spokesman for the Qassam Brigades known as Abu Obeida declared the Egyptian-brokered truce talks dead. He warned foreign airlines not to fly to Ben-Gurion International Airport, outside Tel Aviv, starting from 6 a.m. on Thursday and cautioned Israelis against gathering in large numbers because of the risk from rocket fire.