The Israeli military ordered an estimated 100,000 residents of eastern Rafah to evacuate on Monday.
More than 80,000 people have fled the southern Gaza city of Rafah since Monday, the UN says, as Israeli tanks reportedly mass close to built-up areas amid constant bombardment.
Palestinian armed groups said they were targeting Israeli troops to the east.
Israel’s military has said its ground forces are conducting “targeted activity” in eastern Rafah.
The UN also warned that food and fuel were running out because it was not receiving aid through nearby crossings.
Israeli troops took control and closed the Rafah crossing with Egypt at the start of their operation, while the UN said it was too dangerous for its staff and lorries to reach the reopened Kerem Shalom crossing with Israel.
It came as Israel’s prime minister rejected a threat by the US president to stop supplying some weapons if it launched a major assault on “population centres” in Rafah. Benjamin Netanyahu said Israel could “stand alone” if necessary.
After seven months of war in Gaza, Israel has insisted victory is impossible without taking the city and eliminating the last remaining Hamas battalions.
But with more than a million displaced Palestinians sheltering there, the UN and Western powers have warned that an all-out assault could lead to mass civilian casualties and a humanitarian catastrophe.
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Residents and aid workers in Rafah said the sound of artillery and air strikes was constant on Thursday.
Louise Wateridge, a spokeswoman for the UN aid agency for Palestinian refugees (UNRWA), told the BBC in the afternoon that she was at a health facility in the west and could “hear and feel the bombardment coming closer”.
“The building is shaking on a frequent basis. There is this constant buzzing of drones,” she said. “The fear and nervousness that people [in Rafah] have had, has now become terror.”
Palestinian media said two people were killed on Thursday afternoon in an Israeli air strike in the al-Jneineh neighbourhood – one of the eastern areas which the Israel Defense Forces (IDF) ordered residents to evacuate before beginning its ground operation began on Monday night.
Another three people were reportedly killed in an air strike in the nearby Brazil neighbourhood, which is not in the evacuation zone but is next to the Egyptian border.
Hamas and Palestinian Islamic Jihad (PIJ) – which are proscribed as terrorist organisations by Israel, the US and other countries – said they were targeting Israeli forces on the eastern outskirts with mortars and anti-tank missiles.
Hamas also said it had blown up a booby-trapped tunnel east of Rafah underneath three Israeli military vehicles. The IDF said three of its soldiers were moderately wounded as a result of the explosion.
Overnight, at least five people were reportedly killed when a family’s home in the western Tal al-Sultan neighbourhood was hit in an Israeli strike. They included three children, one of them a one-year-old infant, medics said.
The IDF said on Wednesday evening that soldiers had been carrying out “targeted operations on the terrorist infrastructure surrounding the Gazan side of the Rafah crossing and conducted operational raids on suspicious buildings in the area”, and that about 30 “terrorists” had been eliminated. It also said Israeli aircraft had struck targets in support of the troops.
Gaza evacuation map
The director of the Kuwaiti Specialist Hospital in central Rafah – one of only two hospitals still partially functioning in the city – told BBC Arabic on Thursday that it was facing a surge in casualties, including many “unusual injuries caused by unusual weapons”.
But Dr Jamal al-Hamas said it did not have the diagnostic capabilities to treat them properly, adding: “Even the X-ray machine is disabled due to Israeli shelling and there are no spare parts for it.”
Dr Hams said the situation had been made worse by the closure of the al-Najjar hospital in the city’s east on Wednesday due to an evacuation order and nearby fighting.
The IDF has told displaced people to head towards an “expanded humanitarian area” stretching from nearby al-Mawasi to the city of Khan Younis and central town of Deir al-Balah. It said they would find field hospitals, tents and additional aid supplies. But Palestinians and UN officials said it was made up of neighbourhoods that were overcrowded and lacking in essential services or left in ruins by recent fighting.
Unrwa’s deputy director in Gaza, Scott Anderson, told the BBC that the agency had seen a “significant movement of population, with over 80,00