"The wife of the great leader was martyred with his daughter," in a strike on Tuesday night, Hamas' exiled deputy leader Moussa Abu Marzouk wrote on Facebook on Wednesday.
He said nothing about the fate of Mr Deif himself. He said Israel had been looking for "an excuse to target a big Hamas leader".
Egyptian attempts to broker an end to a month-long war between Israel and Hamas militants collapsed in heavy fighting Tuesday, with Palestinian militants firing dozens of rockets and Israel responding with airstrikes across the Gaza Strip.
