Two Israeli citizens are being held in Gaza, at least one probably by the militant Hamas movement, Israel says.
Avraham Mangisto, of Ethiopian origin, went into the Palestinian territory of his own accord last September and has been missing since then, officials say.
An Israeli Arab is also being held in Gaza, the defence ministry says. Hamas has not commented on either case.
An Israeli soldier, Gilad Shalit, was captured and held by Hamas in Gaza for five years before being freed in 2011.
Israeli defence officials say they have appealed to international and regional bodies to help clarify Mr Mangisto’s situation and are demanding his immediate release.
“According to credible intelligence, Mangisto is being held against his will by Hamas,” a defence ministry statement said.
“Israel will continue to pursue the release and return of the citizen to Israel,” it added.
Israeli President Reuven Rivlin said it was a “painful situation” and that he was in contact with Mr Mangisto’s family.
“This is a humanitarian issue, and we expect those holding him to behave accordingly and return him in good health,” he said.
The Associated Press quoted an unnamed official as saying it was unclear why the 28-year-old went into Gaza but that he was believed to be mentally unstable.
Israeli media said Mr Mangisto, from Ashkelon, had breached the heavily-guarded security fence between Israel and Gaza.
Local media said the Israeli Arab being held in Gaza was a Bedouin from Israel’s southern Negev desert. His name has not been released.
The defence ministry said he had crossed into Gaza several times before.
The two cases were cleared for publication on Thursday after a court lifted a gagging order.
In 2006, Sgt Shalit was captured in a cross-border raid by Hamas, triggering a crisis which was only resolved years later in a controversial exchange for more than 1,000 Palestinian prisoners held by Israel.