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 centre 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 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... The IDF is determined to defeat Hamas and will operate in Gaza City with great determination. For your safety, evacuate immediately, it added.
Israel's security cabinet approved a plan to conquer all of Gaza after indirect talks with Hamas on a ceasefire and hostage release deal broke down in July.
The IDF has been instructed to defeat Hamas after 23 months of war and return the 48 hostages still held by the armed group, of whom 20 are still believed to be alive.
Photographs showed a stream of people moving south along the coastal road from Gaza City on foot, on donkey carts, and in vehicles, but there was no sign of a mass exodus.
The humanitarian situation has become increasingly dire, with UN agencies warning that many households are unable to move due to high costs and logistical challenges.
Despite the order for evacuation, overcrowded temporary shelters and limited aid exacerbate the precarious living conditions for the displaced, contributing to a growing humanitarian emergency.
