A constant barrage of air strikes and tank fire rocked Khan Younis during the night, an AFP journalist said of the main city in southern Gaza that has been the focus of the Israeli attack.
The health ministry said more than 100 people were killed across the occupied Palestinian territory overnight, mostly women and children.
Hundreds of thousands of Palestinians forcibly displaced by Israel have fled south to Rafah since the outbreak of the Israeli war on Gaza, with their tents cramming spaces along streets and in parks.
The city that had been home to 200,000 people now hosts more than half of Gaza's 2.4 million population, the World Health Organization said on Friday.
Witnesses in Rafah said 12 people were killed in an Israeli air strike on a house owned by the Hijazi family.
"They bombed without any warning," said 45-year-old Bilal Jad, a neighbour whose house was damaged in the attack. "There's no safe place anywhere. The air strikes are everywhere."
Civilians who fled to Rafah have been pushed up against the border with Egypt, trying to avoid parts of the city exposed to the fighting in nearby Khan Younis.
One of them, Abdulkarim Misbah, said he fled his home in Jabalia refugee camp in the north and reached Khan Yunis, only to be uprooted once more.
"We escaped last week from death in Khan Yunis, without bringing anything with us," the 32-year-old said.
'Pressure cooker of despair'
The United Nations humanitarian agency OCHA said it was deeply concerned about the escalation of hostilities in Khan Younis, which has pushed more and more people south.
"Rafah is a pressure cooker of despair, and we fear for what comes next," said OCHA spokesman Jens Laerke.
Israeli Defence Minister Yoav Gallant said on Thursday that the occupation army was set to train its sights on Rafah.
"We are achieving our missions in Khan Yunis, and we will also reach Rafah and eliminate terror elements that threaten us," he said in a video message the defence ministry sent to journalists.
Israel has killed at least 27,131 people in Gaza, mostly women and children, according to the health ministry.
The fighting has devastated the narrow coastal strip, while an Israeli siege has resulted in dire shortages of food, water, fuel and medicines.
New push for truce
Image analysis released Friday by the UN satellite centre UNITAR based on footage collected on January 6 and 7 showed "approximately 30 percent" of Gaza's structures had been devastated by the war.
The soaring civilian death toll in Gaza have fuelled calls for a ceasefire, but the US continues to oppose it, backing Israel's brutal war.
US Secretary of State Antony Blinken will travel to the Middle East yet again in the coming days to press a new proposal involving the release of Israeli detainees in return for a pause in the fighting, the State Department said.
Blinken will visit Qatar and Egypt -- the mediators of the proposal -- as well as Israel, the occupied West Bank and Saudi Arabia starting Sunday, it added.
The trip -- his fifth since the war broke out -- comes after Qatar's foreign ministry spokesman Majed al-Ansari said there were hopes of "good news" about a fresh pause to the fighting "in the next couple of weeks".
Ansari said a truce proposal thrashed out in Paris had "been approved by the Israeli side" and received a "positive" initial response from Hamas as well.
But a source close to Hamas told AFP: "There is no agreement on the framework of the agreement yet -- the factions have important observations -- and the Qatari statement is rushed and not true."
US hits Syria and Iraq
A Hamas source said it had been presented with a plan involving an initial six-week pause in fighting that would see more aid delivered into Gaza and exchanges of certain Israeli detainees for Palestinian prisoners held in Israel.
The leaders of Hamas and its Gaza ally Islamic Jihad, Ismail Haniyeh and Ziyad al-Nakhalah, respectively, discussed the latest development and said any future ceasefire must lead to "a full withdrawal" of Israeli troops from Gaza, Haniyeh's office said.
The war has sparked a surge in attacks, against Israel and the US, by groups in the region in support of the Palestinians.
The US army launched a wave of air strikes against Iranian forces and groups in Iraq and Syria on Friday in the aftermath of a drone attack in Jordan that killed three US soldiers on Sunday.
US forces in the Middle East and their allies have faced stepped-up attacks since the war in Gaza began, coming under fire more than 165 times since mid-October.
Friday's air strikes were directed at the Iranian Revolutionary Guard Corps' foreign operations arm, the Quds Force, and "affiliated groups", and hit "more than 85 targets", the US military said.
Also on Friday, the Israeli occupation army said its defence system intercepted a surface-to-surface missile that approached Israeli territory in the area of the Red Sea, with Yemen's Houthi claiming they had fired missiles towards Israel, to force Tel Aviv to stop the war.
Short link: