Hamas leaders on Wednesday said they had agreed to a ceasefire on the condition that Israel reciprocates the action, Reuters reported.
"They have the ability, the control and the power to escalate or to deescalate the situation, to rein in the Palestinian's and their own extremist factions in Hamas or to escalate the situation", said military spokesman Jonathan Conricus.
The military wings of Hamas and the Palestinian Islamic Jihad claimed "responsibility for the striking of military positions and Zionist settlements", saying their strikes were in response to Israeli attacks targeting their positions in recent days.
Islamic Jihad, an Iran-backed Palestinian terror organization, attacked southern Israel Tuesday morning by lobbing between 50 and 60 mortar shells at Israeli towns and communities in what is called the "Gaza belt".
The Israeli military said that by 8pm, militants had fired 70 rockets and mortar bombs into Israel and that three Israeli soldiers were wounded by shrapnel. There were no immediate reports of Palestinian casualties.
Daoud Shehab, an Islamic Jihad spokesman, also said an Egyptian official had been in contact with the group to try to restore calm.
Indonesia strongly condemned Israel's brutal actions against Palestinians during recent border protests held to mark 70 years since the Nakba, when almost one million Palestinians were forced out of their homes to make way for the creation of the state of Israel.
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For his part, however, Energy Minster Yuval Steinitz told Kan Reshet Bet Radio on Wednesday morning that he believes understandings have been reached with Hamas, but Intelligence Affairs Minister Yisrael Katz told the same station that there are no such understandings and no cease-fire.
Palestinians and their supporters say most of the protesters were unarmed civilians and Israel was using excessive force against them.
Tuesday's exchange of fire came after weeks of deadly unrest along the fence between Israel and the blockaded Palestinian enclave. An Islamic Jihad spokesman said "the blood of our people is not cheap".
But Israeli officials deny the Hamas claim.
Approximately 25 of the mortars were intercepted by Israel's missile defence system, he said.
Hamas acknowledged it was mostly a symbolic act.
"Indiscriminate attacks against civilians are completely unacceptable under any circumstances", she said.
The referral sought an investigation into Israeli policies in the occupied West Bank, East Jerusalem and the Gaza since the state of Palestine accepted the ICC's jurisdiction in 2014, Palestinian Foreign Minister, Riad al Maliki said.