Late on Sunday, Palestinians fired 17 rockets into southern Israel in response to the Israeli incursion and air strikes, which Hamas, the dominant Palestinian armed force in the Gaza Strip, said were meant to cover the retreat of a auto used by the Israeli troops.
Early Tuesday, Israeli media reported that a man was found dead under the rubble of a building in the southern coastal city of Ashkelon hit by Gaza rockets.
A picture taken on November 12, 2018, shows smoke rising above the building housing the Hamas-run television station Al-Aqsa TV in the Gaza Strip during an Israeli air strike.
Brigadier-General Ronen Manelis, Israel's military spokesman, said Hamas was "leading Gaza to ruin" and that Israeli attacks on it would "intensify to the degree required".
He added Ashdod and Beersheba "are the next targets if the enemy continues bombing civilian buildings".
A Palestinian laborer from the occupied West Bank was killed when a rocket hit a building in the Israeli city of Ashkelon.
As of Tuesday afternoon, more than 400 rockets fired from Gaza had struck southern Israel. Its Iron Dome rocket defence system intercepted some of the rockets, but a few slipped through.
The cross-border attacks, which were triggered by a botched Israeli undercover raid into Hamas-ruled Gaza over the weekend, marked the most serious escalation since an Israel-Hamas war in 2014. A 19-year-old soldier was critically wounded and rocket attacks and Israeli retaliation fire quickly ensued.
Palestinian officials said that in addition to Baraka, five other Hamas men and a member of the Popular Resistance Committees were killed.
Almost 30 people have been wounded in Israel, three critically, according to medical officials.
As Israel's top ministers gathered in Tel Aviv to discuss the latest flareup of violence in and around Gaza on Monday morning, which threatened to plunge the area into war, the government was rejecting outreach efforts by worldwide mediators. Militants in Gaza responded by launching hundreds of homemade rockets into Israel.
Palestinian fighters in Gaza, including Hamas, issued a joint statement on Tuesday announcing an Egyptian-brokered ceasefire with Israel.
Hamas also canceled a weekly beach protest in northwestern Gaza along the border with Israel.
The escalation of violence has threatened to upend weeks of United Nations and Egyptian-led diplomacy to reach a long-term ceasefire between Israel and Hamas.
There was no word from the security cabinet session whether Israel would agree, and rocket attacks continued amid Israeli air strikes as the forum met.
However, the recent tension since Sunday appears to be escalade since Israeli forces continue to deploy more forces to the border with Gaza.
Among the Israeli targets was Hamas' Al-Aqsa TV building in Gaza, which was destroyed after a series of warning shots were given for journalists to clear the building.
The cross-border fighting came just days after Israel and Hamas reached indirect understandings, backed by Qatar and Egypt, to allow cash and fuel into Gaza. An Israeli Druze lieutenant colonel in the elite Maglan unit, a commando brigade, was killed in the clash, and was hailed as a national hero at his funeral Monday.
Before the flare-up, Netanyahu had defended his decision to allow Qatar to transfer the cash to Gaza despite criticism from within his own government over the move, saying he wanted to avoid a war if it was not necessary.