Abu Obaydah, Hamas' spokesman, has been absent from Hamas video publications since the end of November.
Since Friday, Palestinian Arab media has reported that he was either killed or seriously injured in an IDF attack last week.
Avichay Adraee, the IDF's Arabic spokesman, published Abu Obaydah's picture a few weeks ago after the spokesman had been careful to appear in videos only while wearing a mask.
In his tweet, Adraee wrote "This is Khazifa Kahloott, who hides behind the codename Abu Odaydah, and also behind his red keffiyeh, the same way that Hamas hides behind civilian buildings to launch rockets at Israel."
"He and other Hamas leaders love to hide in their tunnels and behind women and children, as well as behind masks and shadows. You have been exposed. It is time to stop hiding, your mask and keffiyeh will not help you or your organization to hide from the attacks that you are suffering and the fate that awaits all of you who remain."