A spokesman for Israel’s defence ministry said: "According to credible intelligence, Mengistu is being held against his will by Hamas.”
"Israel will continue to pursue the release and return of the citizen to Israel,"
However one Israeli security source quoted in the Times of Israel has claimed that Mr Mengistu is now in Sinai.
The second Israeli has been described as a “young” Arab-Israeli, who has previously entered Gaza, Jordan and Egypt.
Israel confirmed that the two men were being held after a gagging order was lifted at the request of Israeli newspapers Haaretz and Yedioth Ahronoth.
Meanwhile, Hamas held a rally in Gaza to mark the first anniversary of Operation Protective Edge on Wednesday.
At the rally the terrorist group reportedly displayed two new rockets and three dog tags believed to have belonged to Israeli soldiers.
One tag displayed the name and number of Oron Shaul, who was killed during the conflict last summer, but whose his body was never recovered.
