Israel has warned all residents of Gaza City to leave immediately in anticipation of a huge ground offensive.
The military's Arabic spokesman told as many as one million Palestinians living in Gaza's biggest urban center to evacuate southwards. Remaining in the area is extremely dangerous, he said.
On Monday, Israeli Prime Minister Benjamin Netanyahu said air strikes that had destroyed high-rise buildings in Gaza City in recent days were only the beginning of the main, intensive operation to capture what he has described as Hamas's last important stronghold.
Hamas said his remarks amounted to a public demonstration of a fully-fledged crime of forced displacement.
Israel's plan to conquer Gaza City has also brought international criticism.
The UN has warned that an intensification of the offensive on an area where a famine has already been declared will push civilians into an even deeper catastrophe.
The message from the Israel Defense Forces (IDF) - both in leaflets dropped over Gaza City, and posted on social media by its Arabic spokesman Col Avichay Adraee - was unequivocal.
To all residents and those present in Gaza City and all its areas, from the Old City and the Tuffah area in the east to the sea in the west: The IDF is determined to defeat Hamas and will operate in Gaza City with great determination, as it has throughout the Gaza Strip, it said.
Photographs showed a stream of people moving south along the coastal road from Gaza City on foot, on donkey carts and in vehicles on Tuesday, but there was no sign of a mass exodus. Hanaa, a mother of three, told the BBC she did not know where to take her family so she was holding out until they were in real danger.
Razan, a student, said she had fled Gaza City due to the bombardment and was now sharing a room with about 20 relatives in Deir al-Balah.
The UN has reported that more than 97,000 people had been newly displaced since 14 August. However, those able to move south are facing high costs and logistical challenges, with many remaining in Gaza City due to lack of transportation or safe destinations.
Last week, UN agencies said the announcement of intensified Israeli military operations in Gaza City was having horrific humanitarian consequences, calling the situation a potential violation of international law.