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Two Israeli citizens are being held against their will in Gaza — at least one by Hamas, Israeli officials said Thursday.

A government statement said that Avraham Mengistu, 28, independently crossed into the Gaza Strip on September 7, 2014.

"According to credible intelligence, Mengistu is being held against his will by Hamas in Gaza," the statement said, adding that Israel is demanding his immediate release after nearly a year.

The statement also referred to a second case involving an "Israeli Arab ... being held in Gaza" but did not name the individual or provide further details.

However, Prime Minister Benjamin Netanyahu said Israel holds Hamas "responsible" for the welfare of both men.

"I expect the international community, which expresses its concern over the humanitarian situation in Gaza, to issue a clear call for these citizens to be released and to see to their return," he said in a statement.

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Israeli President Reuven Rivlin said he was in touch with the Mengistu family and that authorities have been "working tirelessly" to resolve the "painful situation."

"This is a humanitarian issue, and we expect those holding him to behave accordingly and return him in good health," Rivlin said in a statement. "According to the information which has arisen, Mengistu is being held by Hamas in the Gaza Strip. We will continue to make every effort in order to bring an end to this incident, as soon as possible."

Hamas has not responded to NBC News' repeated requests for comment.

The cases were made public after Israel's military lifted a gag order Thursday and were sure to evoke memories of Israeli soldier Gilad Shalit, who was held captive for more than five years and released in 2011 in exchange for the release of 1,000 Palestinian prisoners.

While it was not immediately clear why the gag order was lifted, the timing was significant: the fatal abduction of three Israeli teens launched the summer war in Gaza exactly one year ago.

Israeli media reported that Mengistu previously was prone to disappearing and suffered from mental illness.

His brother, Ilan, alluded to that at a press conference on Thursday, saying that Mangisto "is not healthy" and urging his release.

"I'm asking the international community to engage and use their power to free my brother," he told reporters. I call Hamas and ask them to take into consideration his health and to release him immediately."

Earlier, father Ayelin Mengistu told Israel's Channel 2 News that his son "used to go missing" for a few days at a time and was depressed after another brother's suicide.

Israeli Cabinet Minister Yaakov Peri told reporters Thursday that Israel had a "moral obligation" to secure Mengistu freedom.

"We know that Mengistu is held by the Hamas," he said. "We are holding Hamas as responsible for holding him. Israel will make every effort to bring him back."