Palestinian civilians told to evacuate eastern Rafah by the Israeli military have described their fear and despair at being uprooted from their homes and shelters, as Israel airstrikes hit Gaza's southernmost city. There were hopes that the Rafah offensive would not go ahead after Hamas accepted a ceasefire proposal on Monday, but those were quickly dashed after Israel said the terms were "far from Israel's necessary requirements" and it would continue "in order to exert military pressure" on the militant group. By Tuesday morning, Israeli airstrikes on Rafah had killed 23 people, including six children, according to hospital officials in southern Gaza. The Israeli military said it had "operational control" of the Gazan side of the Rafah crossing, a vital entry point to transport desperately needed aid into the enclave from its southern border with Egypt. Israel Defense Forces (IDF) spokesperson Nadav Shoshani said on Tuesday the military was undertaking "a precise counterterrorism operation" to "eliminate Hamas terrorists and dismantle Hamas terrorist infrastructure within specific areas in eastern Rafah." Hamas said the Israeli military's move on Rafah constituted a "humanitarian catastrophe" that posed "a direct threat to more than 1.5 million displaced Palestinians." People fleeing the area have told of terrifying experiences while recounting their past 24 hours to CNN, after the Israeli military ordered an estimated 100,000 Palestinians to "evacuate immediately" on Monday. Residents were told to move to Al-Mawasi, a coastal town near the city of Khan Younis that aid groups say is not suitable for habitation. One man, Rabee Gharableh, told CNN that it was his family's seventh displacement. "The situation is very difficult... we left in fear, as civilian houses were being targeted, people we know. The shelling was arbitrary and random last night," he said. Another woman, who did not share her name, said she "fled from death" with her children. She said her family has been displaced over 10 times since the war broke out and had "endured much suffering and humiliation." The current war began on October 7 when Hamas militants killed more than 1,200 people in southern Israel and took more than 200 people hostage. In the almost seven months since, Israel's military bombardment of Gaza has killed more than 34,600 people, according to the Gaza health ministry, and driven more than 1 million Palestinians to seek refuge in Rafah, a city that the medical NGO Medicines San Frontieres said was absent of the "necessary conditions for survival." CNN witnessed people in eastern Rafah in a state of panic following Israel's evacuation announcement, which sparked a flurry of appeals from world leaders, the United Nations, and humanitarian groups urging Israel not to carry out its long-threatened assault. The move was described as "inhumane" by United Nations human rights chief Volker Türk and "beyond alarming" by the Norwegian Refugee Council (NRC). Faisal Barbakh, who fled on his bicycle, said he is leaving a lifetime of memories behind "for the unknown." "I'm carrying all of my life here. My family is torn in seven places. I feel it's the end of life. I can't think anymore. I left 59 years of life behind, all of my memories, my children's pictures, the contract of my house." Video footage shows families arriving to the beach road of Deir el Balah, which is further north than the IDF-outlined humanitarian area, on overloaded trucks, donkey carts and cars. Their vehicles were piled with mattresses and personal belongings, as other people started setting up tents. Many of those leaving eastern Rafah have been previously displaced multiple times as Israel's focus has moved from city to city. "This is the fourth time I'm being displaced. From Nuseirat to Khan Younis, then to Rafah, and now another one. I don't know where I am heading," one man told CNN. After the Israeli military stormed the Rafah crossing, Palestinian flags were replaced with Israeli flags, which according to photos on social media, could be seen mounted outside the main building. IDF spokesperson Shoshani said intelligence indicated that the Palestinian side of the Rafah crossing "was being used for terrorist purposes." The border crossing has been a key humanitarian aid portal, with as many as 300 trucks entering the strip through it each day, according to an announcement from Egypt last month. Wael Abu Omar, a spokesperson for the General Authority of Border and Crossing, told CNN that all movement and aid shipments through Rafah had stopped "after Israeli tanks captured the crossing facilities from the Palestinian side." Gaza's Ministry of Interior and National Security warned that Rafah's closure "exacerbates the humanitarian crisis" and "represents a policy of collective punishment against more than 2 million people." The ministry described the crossing as "a main lifeline for citizens in the Gaza strip" which "does not represent any threat to the Israeli occupation." Aid groups quickly expressed concern that the Israeli operation there could bring humanitarian relief efforts across the Gaza Strip to a standstill. "Continued interruption of the entry of aid and fuel supplies at the Rafah crossing will halt the critical humanitarian response across the Gaza Strip," the UN agency for Palestinian refugees (UNRWA) said on X. It added that the "catastrophic hunger faced by people especially in northern Gaza will get much worse if these supply routes are interrupted." CNN has reached out to the IDF and COGAT on this and asked about any plans to keep aid getting into Gaza. In recent months, Israeli strikes have further deteriorated conditions for those living and sheltering in the city, including an estimated 600,000 children. Malnutrition is rapidly spreading and medical facilities are "rendered ineffective by the Israeli authorities' siege," Medicines San Frontieres said. Two boys, Malek and Yousef, were making their own way of Rafah out on bicycles Monday, clinging to their bags. "We are running away from the Israelis. They warned us and ordered us to evacuate the eastern area. I have my clothes and food in the bag. We are going to our grandparents' house," one said. There has been a chorus of condemnation over the situation facing many in Rafah and other places in the strip after Israel ignored international calls against proceeding with the operation. The European Union's foreign policy chief Josep Borrell warned Tuesday that there were "no 'safe zones' in Gaza" after criticizing Israeli Prime Minister Benjamin Netanyahu. He added that he was "afraid" the offensive would lead to many civilian casualties. Meanwhile, fuel shortages in Rafah have prevented people from fleeing and reaching the Israeli-designated "expanded humanitarian area" in Al-Mawasi, Suze van Meegen, the NRC head of operations in Palestine told CNN by phone from Rafah on Tuesday. Several people in Rafah told CNN that they didn't know where to go. One man, Odeh Asaliyeh, said "death is more dignified than this" and that he "prays to get hit and find rest from all of this." "I don't know where to head to... there is no safe place in all of Gaza" Asaliyeh added. Alaa Abu Ramadan said her family had been waiting for daylight to leave. "We don't know what to do. We are going into the unknown," Ramadan said. For those who are able to travel the many kilometers to Al-Mawasi, the coastal town near Khan Younis, they arrive to find it already crowded with displaced people, some of the new arrivals appearing confused and disorientated. The streets were packed with trucks and donkey carts, surrounded by huge piles of garbage. "I came here from Rafah and didn't find any place to stay. People even say we should leave (here). I swear, I don't know where to go. They distributed leaflets, and people panicked and started running away," said Mohammad Abu Khamash. UNRWA previously warned that Al-Mawasi is not appropriate for habitation. "It's really not somewhere that's quite suitable for people to put up tents and to be able to sit and try to live and meet their basic necessities every day," Scott Anderson, director of UNRWA affairs in Gaza, told CNN Monday. — CNN