In al-Rimal, which is just above Tel al-Hawa on the western side of Gaza City, a freelance cameraman working for the BBC says that he did not receive any evacuation orders, but later learnt that his neighbour did.
He left the area with his family and headed north. They are now in the port area but lack basic necessities. He says he is struggling to find water for his children.
In a statement, the IDF confirmed that it launched what it called a new operation in Tel al-Halwa overnight, following what it said was intelligence of Hamas and Palestinian Islamic Jihad infrastructure and fighters in the area.
The military also said that it was operating at the headquarters of the UN agency for Palestinian refugees, Unrwa, in the area.
The IDF said that at the start of the operation, it gave warnings to civilians – and it said that it would open up a humanitarian corridor for people to leave the area.
The latest Israeli offensive in Gaza comes as hopes have been rising that a ceasefire deal might finally be agreed.
Hamas sources have said they have dropped a key demand – that Israel must accept a permanent ceasefire as a precondition of any potential deal.
Talks have resumed and are expected to continue this week.
But a statement by the office of the Israeli Prime Minister, Benjamin Netanyahu, may have somewhat dampened expectations by insisting that any deal must not stop Israel from resuming fighting in Gaza until its war objectives are met.
Mr Netanyahu has repeatedly defined those aims as being the eradication of Hamas, both militarily and politically.
