Israeli tanks returned to the southern Gaza city of Khan Younis on Friday, forcing families to evacuate along congested roadways.
Thousands of people fled eastern Khan Younis in vehicles and on foot, belongings heaped on donkey carts and motorcycle rickshaws as they made their slow escape along congested roads.
The Israeli military also ordered the evacuation of scores of residents from eastern parts of the city, with videos and images shared online showing exhausted Palestinians making their way to various shelters.
Residents are reportedly evacuating to Al-Mawasi, which Israel has designated as a "humanitarian zone". Despite this, it has been targeted by Israeli in multiple attacks, and is overcrowded by displaced families from around the enclave.
Israel is claiming that there are Hamas operatives in the area, and has vowed to "act forcefully" against them.
This comes after mediators US, Egypt and Qatar have called on Israel and Hamas to resume ceasefire and hostage release negotiations, saying there are "no excuses from any party for further delay".
The countries said talks could take place on August 15 in either Doha or Cairo, adding it was "time to bring immediate relief both to the long-suffering people of Gaza as well as the long-suffering hostages and their families".
Israel's prime minister's office said a delegation would be sent to the talks but declined to give further details. A Hamas official told Reuters the group was "studying" the new offer for talks, refusing to elaborate. The newly appointed overall leader of Hamas, Yahya Sinwar, is believed to run the battle, possibly from the tunnels of Gaza.
Fears are growing of a possible broader conflict. Iran has vowed to retaliate after Hamas's leader Ismail Haniyeh was assassinated in Tehran and Israel killed a top commander of Lebanese militant group Hezbollah in a strike on a Beirut suburb.