The move underlines the difficulties facing the Israeli government as it tries to reconcile its stated aim to "crush Hamas" with saving the lives of as many hostages as possible.
So far, four female hostages have been released after negotiations brokered by Qatar, which is believed to be trying to reach a deal in which 50 more dual nationals held by Hamas would be released.
The Israeli military is using surveillance, special forces raids and interrogation of captured members of Hamas to draw up a picture of where the captives - including infants, children and elderly civilians as well male and female soldiers - are being held.
The leaflets will complement this effort but also seek to sow uncertainty among Hamas supporters about who might have accepted the Israeli offer. Many were torn up immediately by residents in Gaza, witnesses reported.
"If your will is to live in peace and to have a better future for your children, do the humanitarian deed immediately and share verified and valuable information about hostages being held in your area," the military said in the leaflet, which offered security "for you and your home" as well as a reward for any informants.
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