Israel’s military announced air and ground forces were implicated in attacks on Friday but had not penetrated Gaza.
Meanwhile, conflicts between Palestinians and the Israeli security forces scattered across much of the extended West Bank.
At least 122 nationals have been killed in Gaza, and eight have died in Israel since the fighting began on Monday.
Jewish and Israeli-Arab mobs have also been struggling within Israel, assisting its president in warning of civil war.
Defence Minister Benny Gantz commanded a “massive reinforcement” of security forces to overcome the internal unrest of more than 400 people detained.
Police say Israeli Arabs have been accountable for most of the trouble and reject the accusation they are standing by while gangs of Jewish youths target Arab homes.
In Gaza, Palestinians dreading an incursion by Israeli troops have been escaping areas close to the border with Israel. Citizens who had left Shejaiya in Gaza City said projectiles had been falling on homes.
“We felt like we were in a horror movie,” said resident Salwa Al-Attar, who escaped the bombardment with her family. “The planes were above us, and the tanks and navy were bombings – and we could not move. The children, women and men were screaming.”
The Israeli military said it had accompanied an operation overnight to dismantle a network of Hamas tunnels that it dubbed “the metro”, but no troops had entered Gaza. It added that – throughout Thursday evening and Friday daylight – 220 more projectiles were shot from the Gaza Strip.
In southern Israel, an 87-year-old woman succumbed after collapsing on her way to a bomb shelter near Ashdod. Other regions, including Ashkelon, Beersheba and Yavne, were also targeted.
Gaza’s health ministry said 31 children were killed since fighting began, and many other civilians died. Another 900 Gazans have also been injured. Israel says dozens of those executed in Gaza were militants, and some of the deaths were affected by misfired rockets from Gaza.
In a statement published early on Friday morning, Israeli PM Benjamin Netanyahu said the country’s military operation versus Palestinian militants would remain for “as long as necessary”. He appended that Hamas would pay a heavy amount, as would different “terrorist groups”.
A Hamas military spokesman said the organisation was ready to teach Israel’s army “harsh lessons” should it seek a ground incursion.
Also, on Friday, there were protests at the Jordanian and Lebanese borders with Israel in support of the Palestinians. One man died after being hit by Israeli shellfire while protesting, state media in Lebanon reported.
On Thursday, Israel’s military announced up 7,000 army reservists and stationed troops and tanks near its boundary with Gaza. It said a ground invasion into Gaza was one option being weighed, but a decision had yet to be executed.
As fighting registered its fifth day, United Nations Secretary-General António Guterres summoned “an immediate de-escalation and cessation of hostilities in Gaza and Israel”.
His plea echoed that of other diplomats – including from Israel’s ally, the US – but appeals to Israeli and Palestinian leaders have so far declined to produce a ceasefire agreement.
A senior Hamas administrator has stated the group is ready for a “reciprocal” ceasefire if the international community pressures Israel to “suppress military actions” at the disputed al-Aqsa Mosque in Jerusalem.
However, a senior consultant to Mr Netanyahu told the BBC that international requests for restraint were removed.
“We didn’t want this conflict, but now that it’s started, it has to end with a sustained period of quiet,” said Mark Regev. “That can only be achieved by Israel taking out Hamas – their military structure, their command and control.”
Israel has also called up ten reserve border patrol companies to help tackle the worst unrest between Arab and Jewish communities for many years.
Mr Netanyahu has recommended introducing “administrative detention” for radicals. The controversial measure would permit authorities to detain people for elongated periods without charge.
Meanwhile, trials by parties in Israel to form a coalition to replace Mr Netanyahu’s government following inconclusive polls in March appear to have collapsed. It happened after a critical right-wing leader pulled his party out of negotiations, calling the hostilities a “reality changing event”, local media say.
According to reports, Naftali Bennett is now in discussions with Mr Netanyahu’s Likud party to try to form a “broad national unity government”.
Cause of violence
The struggle between Israel and Hamas was triggered by days of intensifying clashes between Palestinians and Israeli police at a holy hill compound in East Jerusalem.
The site is honoured by both Muslims, who describe it as the Haram al-Sharif (Noble Sanctuary), and Jews, for whom it is recognised as the Temple Mount. Hamas commanded Israel to remove police from there and the nearby predominantly Arab district of Sheikh Jarrah, where Palestinian families suffer eviction by Jewish settlers. Hamas propelled rockets when its ultimatum went unnoticed.
Palestinian anger had previously been stoked by weeks of growing tension in East Jerusalem, inflamed by a string of confrontations with police since the commencement of Ramadan in mid-April.
It was further fired by Israel’s annual celebration of its capture of East Jerusalem in the 1967 Middle East war, known as Jerusalem Day.
With its profoundly religious and national significance to both sides, the city’s fate lies at the core of the decades-old Israel-Palestinian dispute. Israel in force annexed East Jerusalem in 1980 and holds the entire city its capital, though the vast bulk of other countries does not acknowledge this.
Palestinians maintain the eastern half of Jerusalem as the metropolis of a hoped-for state of their own.