The protests, now in their fourth week, began on 30 March and will take place until 15 May to mark 70 years since the 1948 Nakba, or 'catastrophe', when more than 700,000 Palestinians fled or were expelled from their homes during the establishment of the Israeli state.
Israeli forces and snipers positioned along the border have killed at least 34 Palestinians and injured thousands more since the protests began.
Seventeen people injured by Israeli snipers have needed amputations of either their lower or upper limbs.
It was the first time leaflets have been dropped in Gaza during recent tensions.
"The Hamas terror organization is taking advantage of you in order to carry out terror attacks. The IDF (Israel Defence Forces) is prepared for all scenarios," the leaflets said.
"Stay away from the fence and do not attempt to harm it."
Human Rights Watch said Israel's deadly response to the mass demonstrations was "unlawful and calculated", with senior Israeli officials green-lighting the use of live ammunition against unarmed demonstrators.
Israeli human rights group B'Tselem has called on Israeli soldiers to refuse orders to open fire on Palestinian protesters in the Gaza Strip.
Israeli defence officials have said the army's open-fire rules would remain unchanged.