Israel dropped leaflets on Gaza City warning residents that the military was about to "escalate" the offensive and to begin a "new phase in the war on terror".
Al Jazeera's Zeina Awad reporting from southern Israel said: "The leaflets are telling people not to associate themselves with Hamas. They're not an order to evacuate like previous ones. An Israeli army spokesperson told Al Jazeera that they were meant to tell Palestinians in Gaza that the offensive will intensify.
"When Israel says they will intensify their operations, they usually do and from the Israeli point of view, we can expect a radical move from the Israeli army, which would mean urban warfare and a higher casualty rate for both sides.
"Putting aside the large number of demonstrations that were held throughout Israel today, the majority of the Israeli public are very much behind their government's decision to intensify their offensive within the Gaza Strip."
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza City, said there had been intense fighting during the day on Saturday.
"The most significant development was the advance of the Israeli military," he said.
"We understand now they are on the outskirts of Gaza City, still trying to avoid going in through major population centres, but navigating their way around those urban areas on the periphery."
Gazans 'locked in'
Mads Gilbert, a Norwegian doctor working at Shifa hospital in Gaza City, told Al Jazeera: "We have been to many war zones, but the special thing is that the 1.5 Gaza population are completely locked in.
"The civilian population has no way to hide. The population density is so high you can not do attacks like this without knowing that you are attacking the civilians.
"Also, the injuries must come from extremely explosive devices. We suspect that Israel is using a new type of high explosive called Dime [dense inert metal explosive].
"We urge the world, stop the bombing of Gaza. Please stop it."
Since Israel launched its offensive 15 days ago, 13 Israelis have died, including three civilians.
Palestinian fighters fired at least 10 rockets into Israel on Saturday, slightly wounding two people.
Al Jazeera's Alan Fisher, reporting from the Gaza-Israel border, said that the number was down significantly over the past two days, from about 30-40 daily since Israel's assault began.
"It may well be that's because the Israeli army is taking over more of the land where these rockets are fired from," he said. "But it also may be that Hamas is running out of rockets to fire into Israel."
"From that point of view, I'm sure the Israeli public believe that this has been a successful operation because it is reducing the capacity of Hamas to fire rockets into southern Israel."
The Israeli military also said on Saturday that it had killed a senior Hamas fighter, who it claimed had supervised rocket launchings.
Amir Mansi was the "leading Hamas authority with regard to the long-range Grad missile launching programme" and commanded a cell in Gaza City that had fired dozens of rockets on southern Israel, the military said in a statement.
A Hamas spokesman confirmed that Mansi was a member of the movement's armed wing but refused to give his rank. He is the son of Yusef Mansi, the minister of telecommunications in Gaza's Hamas-run government.
A senior Hamas delegation was in the Egyptian capital to make their remarks on the Egyptian plan aimed at ending the fighting.
A binding resolution passed by the UN security council late on Thursday failed to bring peace to the Gaza Strip, with Israel arguing that it has the right to self-defence.
Egypt's plan includes an immediate cessation of hostilities for a specified period, the opening of Gaza's crossings, curtailment of arms smuggling into the Strip and attempts at reconciliation talks between the Palestinian factions.
|Gaza's humanitarian situation has only gotten worse as the war continues [GALLO/GETTY]
Mahmoud Abbas, the Palestinian president, also in Cairo, said the Egyptian plan would facilitate progress on a ceasefire.
The UN, meanwhile, has said that it will resume its work in the Gaza Strip after receiving safety assurances from Israeli authorities.
A UN statement said that Israel had given "credible assurances that the security of UN personnel installations and humanitarian operations would be fully respected".
The UN stopped aid shipments after one of its lorries was shot at by Israeli forces, killing the driver, two days ago.
The majority of the 1.5 million people living in the Gaza Strip depend on foreign aid for survival and the humanitarian situation has worsened as the offensive has continued.
"We are receiving reports that some people are starting to burn their furniture to bake bread and to cook," Christopher Gunness, UN relief and works agency spokesman, said on Saturday.