On an eerily deserted street in the al-Karama district of Gaza City, the Abu Sinan family was waiting – in vain – for a taxi. Clutching two blue plastic bags full of clothing and a black backpack, 19-year-old Tariq alternated between scanning the road for a vehicle and casting his eyes to the sky, from where the buzz of Israeli drones could be heard.

Their intended destination was just a few miles across town. "We think it's a safer area," he said. "Here, there is a lot of empty ground. We see the resistance firing rockets every day, so there are a lot of air strikes." He had no idea how long the family would be away from their home: "Until it's over."

A growing number of desperate Gazans appeared to be on the move. One man said that he had taken his wife and baby to Khan Younis, a city in the southern half of the Gaza Strip, in the hope that it was safer.

A woman who took her family to spend the night in a community centre said she had found no respite from the bombing: "We discovered everywhere is equal on the safety scale."

People are beginning to feel like rats in a cage as Israel pummels the tiny territory with missiles and steps up preparations for a possible ground invasion.

The Israeli Defence Forces struck 200 targets overnight; tanks and troops are massing on Gaza's borders; up to 75,000 reservists are being called up. The immediate area around Gaza has been declared a closed military zone.

The psychological impact on Gaza's population of the current offensive is as much a weapon of war as the bombing itself. People in Gaza City say their children are terrified and unable to sleep. Explosions rock the ground and rattle windows throughout the night; daylight brings little respite from the barrage of missiles unleashed on the 1.5 million people crowded into the enclave. Gaza has no public bomb shelters and there is no air raid warning system.

Schools, universities, government offices and most shops have closed. Few people venture far from their homes on foot, and traffic is scarce. The IDF have dropped leaflets over several population areas, warning people to stay away from "the vicinity of Hamas operatives and facilities and those of other terror organisations" for their own safety. There are reports that text messages bearing a similar message have been sent to mobile phones.

But, despite the rising sense of alarm and anticipation at what the coming days might bring, some say efforts to find a safe haven are futile. Ahmed Hatoum, 60, who lives next door to the Hamas headquarters flattened by a powerful air strike at 5am on Saturday, shrugged at the idea of moving his family: "I have no place to go. I'd leave if I could, but in Gaza there is no place to hide."

The danger is not just from Israel. There are reports of militants' rockets falling inside Gaza; the Palestinian Centre for Human Rights said preliminary investigations suggested a missile that killed a four-year-old boy and a 22-year-old man in Jabaliya on Friday may have been fired from within the Gaza Strip.

The stakes are rising. Rockets have reached close to Tel Aviv and Jerusalem, Israel's two major cities, in the last couple of days as Hamas and other militant groups have begun to deploy long-range weapons from their stockpiled arsenals.

"Hamas seems to be going all the way to the brink," said Mkhaimer Abusader, a political scientist at Gaza's Azhar University. "For the past four years, Hamas has been preparing itself for this day." The organisation has built bunkers, improved its military technology and acquired more sophisticated and powerful weapons, principally from Libya. But Israel would not tolerate the launching of rockets at its major population centres, a move which made a ground invasion more likely, he said.

However, sending in troops and tanks also carries risks for Israel. If the goal is to topple Hamas, even more extremist resistance groups could fill the resulting power vacuum. To prevent that, Israel may have to contemplate a long-term reoccupation of Gaza, a step it is reluctant to take. A third scenario – damaging Hamas's infrastructure, deterring its capacity to launch rockets, but leaving the regime in place – would take both sides back to the situation at the end of the last war almost four years ago.

There is also the risk that Israel's actions will result only in support for Hamas hardening. In Jabaliya, north of Gaza City, young boys clambered over a small mountain of masonry chunks, twisted metal and broken glass which, until 6am on Saturday, had been the home of a Hamas official. At the sound of a rocket being fired nearby, the children whooped and cheered.

Nearby, Sharif Khalah, 26, a neighbour of the child and man killed on Friday by a missile that could have been home-grown, said rocket fire from the area was continual. "I support it," he said. "We have to defend ourselves against the enemy. We can't do nothing when they attack us."

Abusader said Gazans were divided. "Those who support Hamas feel very happy that missiles are landing in Tel Aviv. But others are sick and tired, they are exhausted. They are saying they have never recovered from [the last war] and all they want is to live a normal life. It's hard to tell who is in the majority."

In southern Israel, people are also living in fear, jumping at the sound of air raid warnings which give them just a few seconds to reach a bomb shelter or safe room.

Ten people were injured when rockets hit an apartment building and three houses in Ashdod, a city north of Gaza, on Saturday. Two explosions were reportedly heard in Tel Aviv; on Thursday, three Israelis were killed by a missile apparently fired from Gaza.

Abusader said he feared the violence was set to continue for some time yet, despite appeals from the international community.

"The hard fact is that there is no military solution to the Gaza problem," he said. "Israel could kill all the Hamas leadership, but that's not going to put an end to the Palestinian struggle. There has to be a political solution to this. Without that, this conflict is going to go on and on."