Israeli tank fire killed two Hamas gunmen in Gaza on Tuesday in a strike the Israeli military described as return fire for a shooting attack against its forces, an account disputed by the Palestinian Islamist group.
"As of now, approximately 70 rocket launches were identified from the Gaza Strip at Israeli territory", the army said in a statement.
Palestinian health officials said on Wednesday that two of the victims were a pregnant woman and her 18-month old child as the Israeli army claimed it bombed Hamas military targets in the enclave in response to rocket fires..
On Wednesday, UN Middle East envoy Nickolay Mladenov condemned the Hamas rocket fire and called for both sides to step away from the brink.
In a separate statement, the Israeli Air Force (IAF) said its fighter jets targeted 12 terror sites in the Gaza Strip.
Throughout the night, wave after wave of alarms sounded in the Hof Ashkelon, Sha'ar Hanegev and Eshkol regions, outside Gaza, sending thousands of Israelis into bomb shelters, where many bedded down for the night with their families.
Eight rockets were fired from Gaza and four fell into Sderot settlement. The Iron Dome aerial defense system intercepted at least 21 launches that sent rockets heading for densely populated areas in the south; nevertheless, the projectiles that managed to find their targets did considerable damage.
The gathering had raised hopes a deal for a lasting truce with Israel, with the backing of Egypt and the United Nations.
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Tens of thousands of people gathered to honour the victims at an annual memorial ceremony held in the city. But in order to bring this treaty into effect, 50 nations must ratify it, of which only 14 have done so.
A 34-year old man was lightly injured by broken glass, and damages to several cars were reported.
Israel's military on Thursday warned Hamas against a further escalation in violence, and Israeli media said officials were considering evacuating residents from areas near the Gaza border.
Jamie McGoldrick, the United Nations' humanitarian coordinator for the Palestinian territories, in a news release called Israel's restriction of fuel imports "a unsafe practice, with grave consequences on the rights of people in Gaza".
Clashes along the Gaza border since the end of March have seen at least 165 Palestinians killed by Israeli fire.
"The IDF sees with severity the terrorist activities of Hamas", said the army spokesperson in a statement Wednesday night.
One Israeli soldier has been shot dead by a Palestinian sniper during the same period, while incendiary devices attached to balloons and kites launched by Palestinians have sparked hundreds of fires in southern Israel, burning some 3,000 hectares (7,400 acres) of forest and farmland.
The last war in 2014 ended with a tense ceasefire and analysts say another round of conflict remains likely.