The British broadcaster said on Sunday: "We are deeply concerned about what we are hearing - but we stress, at this stage, it is rumour with no independent verification."
The group claiming to have killed him is unknown in Gaza, but the name has been used elsewhere in the Middle East by organisations linked to al-Qaeda.
Hani Kawasmeh, the Palestinian interior minister, said: "This party that issued the statement about the so-called killing is unknown to the security services."
He added: "I have been in contact with all the security chiefs since I heard the information... There is no information to confirm the killing of Johnston until now."
Johnston was snatched at gunpoint in Gaza City on March 12.
Since then there had been no demands or any word on his condition from his captors.
He has been missing longer than any other foreigner kidnapped in Gaza.
One of the few foreign reporters still based in Gaza, he was snatched just weeks before he was scheduled to end his three-year stint there.
Other news organisations withdrew their foreign-born reporters because of the deteriorating security situation there.