Thousands of people have fled the southern Gaza city of Khan Younis after the Israeli military warned of a new operation to flush out Hamas militants that it says have regrouped there.

In al-Jala, a neighbourhood in the south of the city that the Israel Defense Forces had previously designated a humanitarian zone, residents on Sunday packed their belongings, uncertain where to seek refuge. Israel said rockets had been fired from the area.

“We don’t know where to go,” Amal Abu Yahia, a 42-year-old mother of three, told the Associated Press news agency. She took her children to al-Mawasi, a crammed tent camp by the coast, but could not find anywhere to shelter there.

Her husband was killed when an Israeli airstrike hit their neighbours’ house in March, but they had returned to Khan Younis in June to shelter in their severely damaged home. “This is my fourth displacement,” she said.

Vast swaths of Gaza have been bombed to rubble: Khan Younis suffered widespread destruction during the IDF’s months-long battle to take the city at the beginning of the year.

Israeli troops are increasingly being forced to return to areas that had been previous targets for intense fighting, re-engaging Hamas and other militants that have regrouped in urban areas.

The north of the territory is severed from the south by an Israeli military corridor, and the shrinking “humanitarian zones” that Israel says are safe for civilians are already overcrowded. Despite designating some areas as evacuation zones, notably al-Mawasi, the IDF has carried out strikes there.

Philippe Lazzarini, head of the UN agency for Palestinian refugees, said in a post on X: “The people of Gaza are trapped & have nowhere to go. Just in the past few days, more than 75,000 people have been displaced in southwest Gaza.

“Some are only able to carry their children with them, some carry their whole lives in one small bag. They are going to overcrowded places where shelters are already overflowing.”

Israel’s new operation in Khan Younis comes amid speculation that ceasefire negotiations will restart in either Cairo or Doha later this week after calls from the US, Egypt and Qatar for both sides to resume talks. In a statement, the leaders of the three nations, which were instrumental in brokering a week-long ceasefire in November, said there were no excuses “from any party for further delay”.

Israel’s prime minister, Benjamin Netanyahu, said his country would send a delegation to the talks beginning on 15 August, although he has been repeatedly accused of stalling on a deal to ensure his own political survival. Hamas is yet to respond to the invitation.

The renewed push for talks is seen as more vital than ever after last month’s assassinations of a top Hezbollah commander and Ismail Haniyeh, Hamas’s political chief. The killings, in Beirut and Tehran, which both the Lebanese group and Iran have blamed on Israel, threaten to transform the war in Gaza into a region-wide conflict.

Hezbollah and other Iranian allies in the region have said they will stop attacking Israel when the war in Gaza is brought to an end. Almost 40,000 people have been killed in the Gaza Strip in the conflict sparked by Hamas’s 7 October massacre in southern Israel, in which about 1,200 people were killed and 251 taken hostage.

The US vice-president and democratic presidential candidate Kamala Harris said on Saturday that the need for a ceasefire and hostage release deal was urgent.

“The deal needs to get done. It needs to get done now,” she told an event in Phoenix, Arizona. She and President Joe Biden had been working “around the clock” on negotiations, she added.

“Israel has a right to go after the terrorists that are Hamas. But as I have said many, many times, they also have, I believe, an important responsibility to avoid civilian casualties,” she said, in reference to the Israeli bombing of a school being used as a shelter in Gaza City on Saturday that killed about 80 people.

Also on Sunday, the office of the Palestinian president, Mahmoud Abbas, announced that he would visit Moscow next week to discuss the war with the Russian president, Vladimir Putin.

Abbas, who is based in the West Bank, was last in Moscow in February, when Russia hosted reconciliation talks between Abbas’s Fatah, Hamas and other Palestinian factions. Several attempts to heal the rift between Fatah and Hamas since the latter took control of Gaza after a brief civil war in 2007 have failed.