There has been widespread speculation in Israel and Gaza of discussions on a wider peace agreement between the two sides, as tensions have soared in the region over the past few months.
Palestinian Authority Chairman Mahmoud Abbas condemned what he called Israel's "fierce aggression" against the Gaza Strip. One mortar shell landed near a kindergarten shortly before it opened. It said some of the mortars fired were supplied by Iran.
"It all depends on Hamas".
An Israeli tank drives along the border with the Gaza strip, on the Israel-Gaza border, May 29, 2018. The military noted that they will continue to decisively respond with a "wide range of tools" against Hamas actions that threaten Israeli citizens.
Israeli Intelligence Minister Israel Katz sidestepped questions on Wednesday on whether Israel had agreed to a ceasefire but said it was not interested in an escalation toward war.
The attacks continued throughout Tuesday, triggering dozens of rocket sirens in southern Israel and wounding five Israelis, one of them suffering moderate injuries.
The border area has been tense in recent weeks as Palestinians have held mass protests aimed at lifting an Israeli-Egyptian blockade imposed after Hamas seized power in 2007.
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And was 33 when she became only the third player - male or female - to win 20 major singles titles in 2015. Without a seeding, the 23-time Grand Slam champion risks facing highly ranked players in the early rounds.
The last war in 2014 was especially devastating, with over 2,000 Palestinians killed, including hundreds of civilians, and widespread damage inflicted on Gaza's infrastructure in 50 days of fighting.
Hamas is attempting to "turn the border into an active combat zone", Conricus told reporters. "The resistance factions will abide by it as long as the Occupation does the same", Hayya said in a statement, using militant groups' term for Israel.
Regional councils near the Gaza border instructed residents to stay close to bomb shelters.
The United Nations Security Council is expected to meet on Wednesday to discuss the violence, following an American request for an urgent meeting.
The European Union's foreign policy chief, Federica Mogherini, called for an immediate halt to the rocket and mortar fire.
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. More than 800 Jews signed an online letter criticising Board of Deputies' president Jonathan Arkush and president-elect Marie van der Zyl for "failing to place any responsibility on Israel" in the aftermath of the clashes.
Tuesday's exchange of fire came after weeks of deadly unrest along the border between Israel and the blockaded Palestinian enclave.
"The army views the terror activity carried out by the Hamas terror organization with great severity, and will continue to operate in a powerful and determined manner".