The group on Saturday published a photo montage and pictures of 47 hostages with each captioned with the name Ron Arad.
Arad was an Israeli soldier who was taken prisoner after crashing a warplane in Lebanon in 1986.
His fate has been the source of heavy speculation and public concern ever since as his remains have never been found.
A dignified funeral is of the utmost importance for many Israelis for religious and social reasons.
This is especially true for fallen soldiers: the Israeli military has a code that stipulates that soldiers "will not be left behind," neither alive nor dead.
Following Israel's decision to capture Gaza City despite warnings of a humanitarian catastrophe, Hamas has threatened that none of the hostages will return to Israel alive.
About 20 of the 47 hostages were believed to be alive before Israel launched its full operation in Gaza City early on Tuesday, with hostage families warning of the consequences of the decision.
Some hostages have reportedly been moved out of tunnels and distributed across several parts of the city to slow the Israeli advance.
In the photo montage, Hamas accused Israeli Prime Minister Benjamin Netanyahu of refusing to agree to a ceasefire and the release of the hostages.
It also condemns Israeli military chief Eyal Zamir for carrying out the order to conquer Gaza City despite his reported opposition.
The montage is captioned in Arabic and Hebrew with a clear warning: "Due to Netanyahu's refusal and Zamir's submission, a farewell photo for the start of Operation Gaza."
Israeli strikes killed at least 14 people overnight in Gaza City, health officials said.
The strikes come as several countries are increasingly fed up with the intensifying Gaza Strip war, with some moving to recognise Palestinian statehood at the gathering of world leaders at the United Nations General Assembly next week.
In a statement on Friday, Portugal's foreign ministry said it will recognise a Palestinian state on Sunday.
The country had previously announced its plans to do so but has now set an official date.
Portugal is among countries including Australia, the United Kingdom, France, Canada, Malta, Belgium and Luxembourg, expected to recognise Palestinian statehood in the coming days.
The Israeli military, which says it wants to "destroy Hamas' military infrastructure," has not given a timeline for its Gaza City offensive but there were indications it could take months.
In recent days, Israel has been urging hundreds of thousands of Palestinians sheltering in Gaza City to move south to what it calls a humanitarian zone and opened another corridor south of Gaza City for two days this week to allow more people to leave.
with DPA
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