The IDF said the expanded humanitarian area included "field hospitals, tents and increased amounts of food, water, medication and additional supplies".
"An ongoing situation assessment will guide the gradual movement of civilians in the specified areas, to the humanitarian area," it added.
Such messages are unlikely to allay the fears of those living in the city that a wider offensive is on the cards.
The UN agency for Palestinian refugees, UNRWA, which runs the largest humanitarian organisation in Gaza, said the "consequences would be devastating for 1.4 million people" in Rafah.
The organisation added in a post on X, formerly Twitter, that it would not evacuate and would maintain a presence in the city "as long as possible and will continue providing life-saving aid to people".
Ghada el-Kurd, a Palestinian mother-of-two who has been displaced six times over the last four months, told the BBC that she was sheltering only 15 minutes away from one of the areas included in the evacuation order, but was staying put for now.
"I'm so confused, just to be honest. I have no place to go. This was the last place I know," she said.
"If I want to come back to Khan Younis, there is no place - it is all destroyed. [As for] areas of al-Mawasi, they are crowded and I cannot any more live inside a tent."
"Regarding Deir al-Balah and Nuseirat [refugee camp], still there is a lot of air strikes there... and it is a very dangerous area."
James Elder, a spokesman for the UN children's agency, Unicef, who was in Gaza last month, said families now had no choice but to head towards areas that were already overcrowded and lacked basic facilities.
"They will move because they will move or be bombed. But they will move to places where there is no water - not a little bit of water, but no water - and no sanitation," he told the BBC.
For months, Mr Netanyahu has been insisting that victory against Hamas cannot be won without a full-scale offensive in Rafah.
Israel says Rafah harbours four remaining Hamas battalions, amounting to thousands of fighters.
The European Union's top diplomat, Josep Borrell, called Monday's evacuation order "unacceptable".
"The EU, with the international community, can and must act to prevent such scenario," he wrote on X.
US President Joe Biden spoke with Mr Netanyahu abut Rafah by phone on Monday. No details of the call have yet been released.
Officials from Israel and its closest ally, the US, have been holding meetings to discuss alternative, more focused plans. It is not clear if the new evacuation orders are part of those.
In Israel, some families of hostages expressed their fear about what a Rafah operation might mean for their loved ones.
"We are very much afraid that the IDF entering Rafah will risk the lives not only of innocent people, not only of soldiers, but also of some hostages," said Gil Dickmann, whose two cousins were taken hostage on 7 October, one of whom was released and the other remains in captivity.
The current war began when Hamas fighters stormed into southern Israel on 7 October, killing about 1,200 people and seizing more than 250 hostages.
The Israeli response has seen intense bombardment of all parts of Gaza from the air and a ground invasion that has seen troops take control of most of the territory before withdrawing most troops. More than 34,735 Palestinians have been killed, according to the territory's Hamas-run health ministry.
A deal agreed in November saw Hamas release 105 hostages in return for a week-long ceasefire and some 240 Palestinian prisoners in Israeli jails. Israel says 128 hostages remain unaccounted for in Gaza, at least 34 of whom are presumed dead.