Dozens of Israeli tanks moved into southern Gaza on Monday as the Israel Defense Forces (IDF) hit the main city of Khan Younis with airstrikes and urged residents to flee.

The bombardment came as the IDF said it was operating against Hamas targets “in all of the Gaza Strip”.

“The forces are coming face-to-face with terrorists and killing them,” Rear Admiral Daniel Hagari told reporters in Tel Aviv.

Israel’s military posted a map on Monday morning with around a quarter of the city of Khan Younis marked off in yellow as territory that must be evacuated at once.

Three arrows pointed south and west, telling people to flee 20 numbered blocks and head further towards the Mediterranean sea and the Egyptian border.

It came as the commander of Israel’s armoured corps said that his and other ground forces were close to achieving their war mission in the northern Gaza Strip.

Many of those who have taken shelter in Khan Younis were displaced from other areas in the central and northern Gaza Strip during the first phase of Israel’s ground offensive.

Israel said it was defining “safe areas” in order to minimise civilian casualties, but UN officials and Palestinians warned it was difficult to heed the orders in real-time given patchy internet access and unreliable electricity.

Aid groups demanded an immediate ceasefire, saying civilians had nowhere to hide from the conflict.

Israel said it was not seeking to force Palestinian civilians to permanently leave their homes, even as it acknowledged conditions in Gaza were “tough”.

“We have asked civilians to evacuate the battlefield and we have provided a designated humanitarian zone inside the Gaza Strip,” said Jonathan Conricus, a spokesman for the IDF, referring to a tiny coastal area of the territory named Al-Mawasi.

Any suggestion of Palestinian dispersal is highly contentious in the Arab world as the war that led to Israel’s creation 75 years ago gave rise to the exodus or forced displacement of 760,000 Palestinians.

The UN currently estimates that around 1.8 million people in Gaza, roughly 75 per cent of its population, had been displaced, many to overcrowded and unsanitary shelters in the south.

James Elder, a spokesman for Unicef, said Khan Younis had endured a “night of utterly relentless bombardments”.

“I don’t think there was more than a five or 10 minute period throughout the course of the night where something wasn’t flying overhead or the sky being lit up,” he said.

Save the Children warned “there is nowhere safe” in the coastal territory as Israel intensifies its military operations.

“Families are being warned by Israeli authorities to move, once again, forcibly displacing them into smaller and smaller areas with no guarantee of safety or return, and without the necessary infrastructure and access to services to support life,” said Jason Lee, the charity’s country director for the Palestinian territories.

“Rather than the sham pretence that these orders ensure the safety and survival of families, they instead present families with the inconceivable ‘choice’ of one death sentence over another.”

Civilians who had already fled the north were desperate, with many of those on the move lugging their few remaining belongings away in plastic bags and on wooden carts.

Samia Adel, a 39-year-old doctor, said she was desperate to escape Khan Younis but had no idea where to go.

“I don’t know what I’m doing … it’s a nightmare,” she said.

“I’m looking for somewhere to go. I thought they would have allowed us to return to Gaza City when they started in the south. I can’t find words to describe how I feel. It’s grim.”

‘Your indifference ... is a disgrace’

Meanwhile in Israel, families of the remaining hostages were pressing the government to resume talks to save their relatives.

Daniel Lifshitz, the grandson of kidnapped Oded Lifshitz and Yocheved Lifshitz, who was later released from captivity, said relatives were urging the cabinet to go back to talks “without any delay and at any costs”.

“Your indifference towards us is a disgrace,” he told reporters.

Oded, 83, remains missing, presumed to be one of the estimated 140 captives still being held in the Gaza Strip.

Families of the hostages planned to stage a sit-in outside the IDF headquarters in Tel Aviv on Monday evening and stay there until talks are resumed.

Under an agreement between Israel and Hamas, 80 Israeli hostages were released in exchange for three times as many Palestinian prisoners during a seven-day truce that ended on Friday. Another 25, mostly Thai citizens, were freed separately.