An Israeli army spokesman says fierce battles are raging at Hamas’s new strongholds in the Gaza Strip.
The Israeli military has vowed to continue its operation in Gaza, but admitted it is “protracted” and “difficult”.
A spokesman said over the weekend it was expanding its “ground operations in the southern and northern Gaza Strip”.
Meanwhile, the US said Joe Biden spoke to the Israeli PM and emphasised the “critical need” to protect civilians.
In response, Benjamin Netanyahu said the war would go on until all Israeli goals were achieved.
President Biden also told reporters that he had not asked Mr Netanyahu for a ceasefire.
On Friday, the UN Security Council approved a resolution demanding large-scale aid deliveries to Gaza – but stopped short of calling for a ceasefire between the two warring sides.
Talks held in Egypt earlier this week designed to secure a fresh truce between Israel and Hamas have so far failed to deliver results.
A Palestinian official familiar with the ceasefire negotiations has told the BBC that Egypt presented a new three-stage plan that begins with a two-week humanitarian truce which could be extended, during which Hamas releases 40 hostages and Israel releases 120 Palestinian prisoners.
This stage would be followed by the formation of an independent body to deal with humanitarian relief and reconstruction, as well as a comprehensive ceasefire and an exchange of prisoners.
The Hamas-run health ministry says more than 20,000 people have been killed and 53,000 injured in Gaza since the war began. Most of the dead are women and children, Hamas says.
Israel says it takes steps to avoid civilian casualties, and blames Hamas for embedding itself in densely-populated areas.
Meanwhile, the IDF has announced that 13 of its soldiers have been killed in fighting in Gaza since Friday, bringing the total to 154.
Israel says 700 Palestinian militants have been arrested since it launched its military operation and invasion of Gaza with the aim of eliminating Hamas.
The Israeli operation began after Hamas fighters crossed from Gaza into southern Israel on 7 October, killing 1,200 people and taking about 240 hostages.
In a separate development on Saturday, Mr Netanyahu and Mr Biden discussed in a phone call Israel’s operation in Gaza.
Mr Biden “emphasised the critical need to protect the civilian population including those supporting the humanitarian aid operation, and the importance of allowing civilians to move safely away from areas of ongoing fighting”, the White House said.
Mr Netanyahu “made it clear that Israel would continue the war until all of its goals have been achieved”, the Israeli PM’s office said.
In its update on Saturday, the Hamas-run health ministry said another 201 people had been killed and 368 others injured in the previous day alone.
The Israeli military has kept up its bombing campaign in Gaza – ordering civilians to flee.
On Saturday, it said one of its fighter jets had killed Hassah Atrash, a man it accused of smuggling weapons into Gaza to arm Hamas. There was no confirmation from Hamas.
The Israeli military has said it has almost full operational control of the north of the Gaza Strip, and is stepping up operations in the south.
The UN said the latest evacuation order affected 150,000 people in the middle of the territory.