Fierce fighting was reported in Jabalia in northern Gaza after the Israeli military returned to areas where it said Hamas had regrouped.
Residents who fled said they saw tanks advancing towards the Jabalia refugee camp, which has been under heavy shelling since Saturday.
Palestinian armed groups also said they were fighting troops in the field.
Meanwhile, the UN said 360,000 people have fled Rafah in the south since an offensive began a week ago.
The Israeli military ordered the evacuation of the eastern third of the city, which is swollen with more than a million Palestinian refugees.
On Sunday, US Secretary of State Antony Blinken warned Israel that a full-scale offensive in Rafah could provoke “anarchy” without eliminating Hamas.
His comments reflected information relayed to the Israeli media by unidentified Israeli military figures, who stated that the resurgence of Hamas in northern Gaza was due to the Israeli government’s lack of a specific plan for the “day after” the war.
The military reduced operations in the north in January, after declaring that it had “dismantled” Hamas battalions in that country. But this left a power vacuum in which the group managed to rebuild itself.
An estimated 300,000 people trapped in the devastated region are also experiencing “total famine” due to a lack of aid delivery, according to the head of the World Food Programme.
Residents who were filmed fleeing Jabalia on foot on Monday morning said they decided to leave after seeing tanks advancing in the area.
“We don’t know where to go. We have been moved from one place to another,” one woman told Reuters news agency. “We’re running through the streets. I saw it with my own eyes. I saw the tank and the excavator.”
The military wings of Hamas and Palestinian Islamic Jihad – which are both banned as terrorist organizations by Israel, the UK, the US and other countries – said their fighters were attacking Israeli forces in and around the Jabalia camp with mortars. , anti-tank missiles and machine guns. weapons.
The Hamas-affiliated Safa news agency also reported clashes between Palestinian armed groups and Israeli tanks east of the Jabalia camp market, near several UN-run schools that were being used as shelters by civilians.
The official Palestinian news agency Wafa, however, reported that two people were killed in Israeli attacks on homes in the Jabalia camp on Monday and that several other people were killed in an attack in the town of Jabalia.
It also cited ambulance crews who said the bodies of 20 civilians had already been recovered in Jabalia and taken to Kamal Adwan hospital in Beit Lahia.
There was no immediate comment from the Israel Defense Forces (IDF).
On Sunday, the IDF said troops began an operation in Jabalia the night before “based on intelligence information about Hamas’ attempts to reassemble its terrorist infrastructure and operatives in the area.”
It happened after civilians were told to evacuate to the west of Gaza City.
The IDF also said it was operating in the Zeitoun area, east of Gaza City, to “eliminate terrorists and dismantle terrorist infrastructures.”
Safa reported that Zeitoun was hit by Israeli shelling on Monday morning.
The UN agency for Palestinian refugees, Unrwa, said the bombing and evacuation orders had “created further displacement and fear for thousands of families” in northern Gaza.
Unrwa also warned that affected civilians, like the estimated 360,000 who fled Rafah last week, had “nowhere safe to go”.
After seven months of war in Gaza, Israel has insisted that victory is impossible without taking Rafah and eliminating the last remaining Hamas battalions. But the UN and Western powers warned that an all-out attack could lead to mass civilian casualties and a humanitarian catastrophe.
There have been scenes of despair in Rafah since the IDF said last Monday it was beginning a “precise operation against Hamas” in eastern Rafah.
On Saturday, leaflets were distributed ordering residents to evacuate neighborhoods further east, including those close to the city center.
Unrwa deputy director in Gaza, Scott Anderson, based in western Rafah, told the BBC on Monday that the Israeli operation now extended “about a third of the way through Rafah” and encompassed the old city.
He said he could hear explosions and airstrikes, and that the fighting had affected the operations of hospitals and many of Unrwa’s facilities in the Rafah refugee camp, including a primary health facility.
Palestinian media reported that four people, including a child, were killed on Monday in an Israeli airstrike on a house in the Brasil neighborhood, which is southeast of the camp.
Hamas’ military wing also said it was targeting Israeli forces east of Rafah.
Many people sheltering in central and western areas that are not subject to evacuation orders have also left out of fear that the Israeli operation will soon expand into a full-scale offensive.
Ghada el-Kurd, a mother of two, told the BBC on Monday that she recently fled to Deir al-Balah in central Gaza – the seventh time she has been displaced during the war.
She said the streets of Deir al-Balah were “full of sewage” and that the destruction of homes and infrastructure was “huge, not like Rafah”.
She added: “I’m lucky to have a house, but most other people live in tents and [suffering from] the heat, the lack of water and the lack of food.”
Deir al-Balah is part of the IDF-designated “expanded humanitarian area”, which extends north from the coastal strip of al-Mawasi to the city of Khan Younis and the Central Gaza Area.
The IDF told evacuees they would find field hospitals, tents and relief supplies there, but Unrwa’s Anderson said it lacked the necessary infrastructure.
In al-Mawasi, he explained, “everything people have access to has to be transported by truck… which includes food, water and movement of solid waste.”
“For the people who are moving to Khan Younis it is very similar… They are still recovering from the Israeli operation that took place a few months ago.”
Anderson also called on Israel and Hamas to agree to the creation of a “fixed corridor” that would allow UN trucks to safely enter and exit the nearby Kerem Shalom border crossing with Israel – a key entry point for aid.
Israel said it reopened the crossing last Wednesday after closing it for four days due to Hamas rocket fire. But the UN said it was too dangerous to collect aid due to hostilities in eastern Rafah.
The Rafah border crossing with Egypt has also been closed since Israeli troops took full control of the Palestinian side last Tuesday.
In a statement released on Sunday, Hamas accused Israel of “increasing its brutal massacres in several areas of the Gaza Strip”.
Israel launched a military campaign in Gaza to destroy Hamas in response to the group’s cross-border attack on southern Israel on October 7, during which around 1,200 people were killed and another 252 were taken hostage.
More than 35,090 people have been killed in Gaza since then, according to the territory’s Hamas-run Ministry of Health.
