The Israeli army said on Saturday about 300,000 people have left eastern Rafah for a humanitarian area since it ordered an evacuation of the southern Gaza city this week.
"So far, approximately 300,000 Gazans have moved towards the humanitarian area in Al-Mawasi" since the order was issued on Monday, the military said in a statement.
On Friday, the United Nations said more than 100,000 people had fled Rafah in recent days.
The army's calls for a "temporary evacuation" were being communicated to people through leaflets, mobile text messages, phone calls and broadcasts in Arabic, its statement said.
The military ordered the evacuation of eastern Rafah on Monday as it seized control of the crossing with the Egyptian border ahead of its long-threatened ground assault in the city where some 1.4 million people are sheltering.
Earlier on Saturday the military ordered people to leave more areas in eastern Rafah and northern Gaza Strip as it pressed ahead with its fight against Hamas militants.
The evacuation orders and the army's intense bombing of eastern Rafah have raised widespread international alarm.
Meanwhile, the Israeli military on Saturday ordered Palestinians to leave more areas of eastern Rafah and the northern Gaza Strip as it pressed ahead with its fight against Hamas militants.
The latest evacuation order, which some residents told AFP they had received via text and audio messages to their phones, comes days after Israeli tanks and troops entered Rafah, the Palestinian territory's southernmost city, and seized a key crossing on the Egyptian border.
Residents and displaced Gazans were told to leave parts of Rafah's Shabura refugee camp, administrative area, Jenina and Khirbet al-Adas neighbourhoods, and head to the coastal "humanitarian area" in Al-Mawasi.
Aid groups and UN officials have warned that the area was already overcrowded and not ready to receive an influx of people.
Israeli military spokesman Avichay Adraee posted the order in Arabic on social media platform X, saying these areas had "witnessed Hamas terrorist activities in recent days and weeks".
Images on social media showed leaflets with the latest order, which the army said in a statement it had distributed in the affected areas.
Suhaib al-Hams, a hospital director in Rafah, said in a video message to journalists that "sadly, the Kuwait Speciality Hospital is now included in the places threatened with evacuation."
"There is no other place for patients and injured people to go to but this hospital," Hams said, urging "immediate international protection" for the medical facility.
The Israeli army on Monday issued its first evacuation order for parts of eastern Rafah, saying it was in preparation for a widely anticipated ground assault.
Israeli officials have repeatedly vowed to sent ground troops into Rafah, where the majority of Gaza's 2.4 million people have sought shelter, saying there were four Hamas battalions in the southern city that needed to be dismantled.
Adraee said in his statement that evacuation orders were also issued to Palestinians in northern Gaza's Jabalia and Beit Lahia, areas that saw intense fighting in the early stages of the seven-month war.
"You are in a dangerous combat zone," Adraee said.
"Hamas is trying to rebuild its capabilities in the area, and therefore the IDF (army) will work with great force against terrorist organisations in the area."
Israeli forces have repeatedly targeted Jabalia and Beit Lahia, as well as other parts of northern Gaza, since the army launched its ground operation in the besieged on October 27.
Israel's massive military campaign in Gaza began after Hamas carried out an unprecedented attack on southern Israel on October 7 that resulted in the deaths of more than 1,170 people, mostly civilians, according to an AFP tally of official Israeli figures.
Israel's retaliatory campaign has killed at least 34,943 people in Gaza, most of them women and children, according to the Hamas-run territory's health ministry.