The United Nations said it had been informed of the order shortly before midnight but as thousands of people streamed southwards in cars and on foot, the Israeli army admitted that the evacuation would "take time".
Herewith the main reactions so far:
While the US said that it did not put any conditions on the way Israel can use the weapons it provides for fighting the Palestinians, with American President Joe Biden, repeatedly giving staunch support for Israel, Biden said that addressing the humanitarian crisis in Gaza was a "priority."
"We can't lose sight of the fact that the overwhelming majority of Palestinians had nothing to do with Hamas, and they're suffering as a result as well," Biden said during a speech in Philadelphia.
Earlier the White House said the evacuation demand was a "tall order".
"It's already a combat zone. So I don't think anybody's underestimating the challenge here of effecting that evacuation," National Security Council spokesman John Kirby told CNN.
Secretary of State Antony Blinken who earlier told Israel "You may be strong enough on your own to defend yourself, but as long as America exists, you will never, ever have to. We will always be there by your side", is working with Israel "on the need to establish some safe areas where civilians could relocate" a US official said, opting to call Israel's grisly bombardment of the Palestinian enclave a "legitimate security operation."
Russia's President Vladimir Putin compared Israel's siege of Gaza to the Nazis' World War II blockade of Leningrad.
"Various scenarios are emerging, including the possibility of military and non-military measures being taken against the Gaza Strip comparable to the siege of Leningrad during World War II," Putin told journalists in Kyrgyzstan.
"We understand what that entails. In my opinion, this is unacceptable. More than two million people live there," he added.
UN chief Antonio Guterres appealed for the protection of basic human rights and stressed that "even wars have rules", ahead of a Security Council meeting on the volatile situation.
He said the situation in Gaza had reached "a dangerous new low" and called for immediate humanitarian access through Gaza to get "fuel, food and water to everyone in need."
He said the blockaded enclave's health system was on the brink of collapse.
The UN described such a population transfer in so short a timescale as "impossible" and urged Israel to rescind the order. It announced it was relocating its agency for Palestinian refugees and foreign staff to southern Gaza.
The International Committee of the Red Cross said Gaza Palestinians had "nowhere safe to go" and it was "impossible" for them to know which areas "will next face attack".
With a military siege in place, humanitarian organizations "will not be able to assist such a massive displacement of people in Gaza".
Palestinian president Mahmoud Abbas warned of a "second Nakba", a reference to some 760,000 Palestinians who fled or were expelled from their homes during the 1948 war that coincided with Israel's creation.
Abbas said he "completely rejects the displacement of our people from the Gaza Strip, because it will be tantamount to a second Nakba for our people".
The Cairo-based Arab League condemned a "forced transfer" that constitutes "a crime".
Leader of the organization Ahmed Aboul Gheit accused Israel of carrying out "an atrocious act of revenge... punishing helpless civilians in Gaza," rather than a "planned or studied military operation" on uprooting Hamas militants over their attacks on Israel.
Egypt's President Abdel-Fattah El-Sisi urged Gazans to "stay steadfast and remain on their land", as Egyptian security sources warned that some parties and forces plan to forcibly displace Palestinians from their land.
US officials said they were in talks with Egypt to open the Rafah crossing to foreign nationals who want to flee.
Germany's Foreign Minister Annalena Baerbock condemned Hamas for taking "the entire population of Gaza hostage". She accused Hamas of "barricading itself behind more innocent people and is using them as a shield", without providing any proof for such claims.
Saudi Arabia denounced the displacement of Palestinians from Gaza and attacks on "defenseless civilians", in its strongest language criticizing Israel since the war broke out.
Riyadh "affirms its categorical rejection of calls for the forced displacement of the Palestinian people from Gaza, and its condemnation of the continued targeting of defenseless civilians there," the foreign ministry said in a statement.
Turkey called the evacuation demand "unacceptable".
"Forcing the 2.5 million residents of Gaza, who have been subject to indiscriminate air strikes for days and deprived of electricity, water and food, to migrate in an extremely limited area is a flagrant violation of international law and is inhumane," the foreign ministry said in a statement.
World Health Organisation
The WHO joined other UN bodies in calling for Israel to rescind the evacuation order.
"A mass evacuation would be disastrous -- for patients, health workers and other civilians left behind or caught in the mass movement," it said.
Palestinian officials told the WHO that moving vulnerable hospital patients to the southern Gaza Strip was "impossible".
Hospitals in the south of Gaza were already "overflowing", WHO spokesman Tarik Jasarevic said in Geneva. "With ongoing airstrikes, civilians have no safe place left to go".
Organization of Islamic Cooperation
The Organization of Islamic Cooperation accused Israel of seeking to "forcibly displace the Palestinian people" and seeking to shift "the humanitarian crisis... to neighbouring countries".
*This story was edited by Ahram Online