The silver estate car was heavily laden, its rear suspension visibly stressed as it moved up one of the two main roads running the length of Gaza.

On a shabby A-road just south of Gaza City, the driver appears to see an Israeli tank hidden to his right before executing a hasty three-point turn to escape.

But it is too late. Before he can speed away, the car is hit broadsides by a tank shell at near point-blank range. The vehicle vanishes, together with its occupants and whatever it was carrying in a single terrifying blast.

A video of the incident - the latest in the graphic new genre of “war porn” being disseminated through unofficial and official channels alike - was widely circulating on social media on Monday, and cited as evidence of Israel’s expanding reach on the ground in Gaza.

Rear Adm Daniel Hagari, the Israel Defense Forces (IDF) spokesman, declined to comment on specifics but confirmed Israel had “expanded the activity” of its forces within Gaza, bringing in “infantry, engineering corps, armoured tanks and artillery corps”.

“There is also direct contact between our forces on the ground and terrorists as the fighting continues inside the Gaza Strip,” he confirmed.

Israeli intelligence analysts describe the IDF’s push into Gaza not in terms of shock and awe but as a “cautious, step-by-step” push which is designed to balance competing pressures and priorities.

The same tone was struck by Benjamin Netanyahu, the Prime Minister, who told his war cabinet on Monday that Israel is making “systematic progress” in its military campaign against Hamas.

The Israeli army “has expanded its ground entry into the Gaza Strip, it is doing it in measured, very powerful steps, making systematic progress one step at a time”, he said.

After weeks of heavy bombing and several night raids designed to test Hamas resistance, disarm booby traps and roll the field, Israel now has troops dug in on the strip and appears to be trying to draw a noose around Hamas by cutting the strip in two.

Its troops are moving in from above Gaza City in the north and up from towards Wadi Gaza in the south, potentially laying siege to Hamas’s main military assets and infrastructure.

It was speculated that the Israeli tank in the video was part of this, severing one of the two main roads running south to block supply lines and prevent Hamas’s escape.

The only other main road south through Gaza is situated close to the coast and can be covered by gunships in the Mediterranean.

“They have cut the Salahedin road and are firing at any vehicle that tries to go along it,” one local resident was quoted as telling the Associated Press.

For more than two weeks now, Israeli commanders have been calling for civilians in Gaza to move south of Wadi-Gaza for their own protection. Although close to a million Gazans have since moved south, tens of thousands more are believed to remain in the north where the bombing has been most intense.

Now with Israeli troops and armour moving in on the ground, it is unclear how long the window for escape will remain open, if it has not already closed.

Fadi, who lives in the Jabalia refugee camp on Gaza City’s northern outskirts and declined to give his last name, said the area was now in mortal danger from Israel’s ground offensive with tanks rumbling on its fringes. But he vowed not to leave.

“The entire place here is full of people. No one in the entire neighbourhood has left. We are staying,” he told Reuters by phone. “Whether tanks or planes, there will not be another displacement (of Palestinians). That is our decision even if that will mean our martyrdom (death).”

Islamic Jihad, which is fighting alongside Hamas in Gaza, said in a statement that now was not the time for a ceasefire. “Our duty today is fight and fight,” it said.

The IDF said it had hit “more than 600 targets in the past 24 hours”, up from 450 the previous day.

“IDF troops killed dozens of terrorists who barricaded themselves in buildings and tunnels, and attempted to attack the troops,” it added.

Hamas itself reported “heavy fighting” in northern Gaza but said Israeli tanks had retreated from the southern outskirts of Gaza City.

“There’s absolutely no ground advance inside the residential neighbourhoods in the Gaza Strip. What happened on Salah al-Din Street was the incursion of a few occupation army tanks and a bulldozer,” said Salama Maarouf, the head of the Hamas government office in Gaza.

“These vehicles targeted two civilian cars on Salah al-Din Street and bulldozed the street before the resistance forced them to retreat’.

Israeli analysts say the IDF’s “step-step” strategy is being shaped by a range of competing demands.

The first is the lesson of the 2014 war in the territory when, during 50 days of hostilities, 66 Israeli soldiers were killed as a result of Hamas’s use of booby traps and tunnels.

One of the most deadly incidents occurred in Gaza City on the third day of the conflict when an armoured personnel carrier broke down and was hit by an anti-tank rocket.

All seven soldiers inside were killed and, in the aftermath, Hamas fighters gathered the remains of one which they are still holding.

It was only after this incident that overwhelming artillery bombardments and air strikes were called in by the IDF.

“The IDF learns from its mistakes and that is why you have seen air strikes over such a period; they are preparing the ground, clearing it in the areas where they know they will have to fight,” one former military intelligence analyst told The Telegraph on Monday.

Manuel Trajtenberg, executive director of the Institute for National Security Studies (INSS) in Tel Aviv, said the IDF’s strategy also had to take account of “several different clocks, all of them ticking down”.

“There’s the military clock itself in terms of manpower and capacity but also the hostages, international pressure and even economic pressures,” he said. “The biggest challenge is how these can be synchronised.”

The stated objective of the IDF in Gaza is to destroy the military wing of Hamas and its vast military infrastructure including its tunnel network, missile production facilities and arms and fuel stores.

Fuel is being used not just to constantly ventilate the tunnel system but to pump out water because some of the tunnels go beneath the water table, he said.

Having flattened most of the areas of Gaza City in which it believes it is most heavily dug in from the air, the IDF is now slowly moving troops forward, bulldozing tunnels as it goes in a bid to try and prevent surprise attacks from its rear.

Bunker-busting bombs which can penetrate 100 feet below the surface were used on Friday, lighting up the skies for miles around before the troops moved in over the weekend.

“Only the IDF knows fully what is going on but it seems slow and deliberate,” said Sima Shine of the INSS. “I would characterise it as a cautious, step-by-step approach from a military perspective.”

Mr Trajtenberg predicted the Israeli ground operation would “peak in two weeks and then diminish gradually with a long tail” stretching into months.

More aid would probably start to flow into the south but only a deal over hostages would now be likely to alter the trajectory of Israel’s incursion in the north, he said.

Ultimately, Hamas would be destroyed or expelled and Gaza would be run by surrounding Arab nations, perhaps with UN involvement, until the Palestinian Authority could take over, he suggested.

Although the world is focused on Gaza, there is an urgent debate within Israel’s security apparatus about what should be done to contain Hezbollah in the north.

With more than 150,000 rockets, modern weaponry supplied by Iran and recent combat experience in Syria, all agree it is a much greater threat from a military standpoint than Hamas ever was.

Since the massacre on Oct 7, there have been daily skirmishes along the border with 20 to 30 Hezbollah guard posts destroyed, foliage burnt back to make surprise attacks more difficult and up to 60 Hezbollah fighters killed by Israeli artillery and air strikes.

Israeli shelling has expanded in recent days, including a strike on Saturday on Jabal Safi, a mountainous area that lies about 25 km (15 miles) into Lebanon.

On the Israeli side, a total of 30 communities housing nearly 30,000 people have been evacuated in case of attack, placing further considerable stress on the country’s housing and economy.

“For more than a decade we have calculated that there was a deterrence equation which meant it was in neither side’s interest to escalate in the north, but now we have to confront this huge military challenge, equipped as it is with cyber drones, guided rockets and even air defences,” said Orna Mizrahi, a senior researcher at the INSS.

Immediately after Oct 7, many within the IDF and wider Israeli intelligence community argued for a preemptive strike on Hezbollah, she added. Now, however, with US aircraft carriers within striking distance, a “Gaza first” strategy has been adopted.

“The focus now is on the south - on the destruction of Hamas - which it is hoped will provide a deterrent to Hezbollah,” said Ms Mizrahi. “After that Israel will have to rethink our strategy in the north to make sure we don’t repeat the mistake we made with Hamas.”

Ms Shine and Ms Mizrahi agree that lurking behind all of this is Iran which funds Hamas, Hezbollah and several other proxies in the region as part of its so-called “Axis of Resistance”. And this too is a threat they believe Israel and the wider West will eventually have to deal with.

“Iran is the problem; they are happy and they are celebrating,” said Ms Shine. “We were focused on the nuclear threat and became distracted from the conventional military build-up via its proxies.

“Eventually Israel and the West will have to confront Iran and its proxy factory.”