Israel says its troops are in "the heart of Khan Younis" after bombarding the southern city overnight.
The Israeli military report "the most intense day" of fighting since their ground operation began in late October.
The resumption of fighting has intensified the hunger crisis in Gaza, the UN Food Programme says.
According to the head of the Norwegian Refugee Council, the "pulverising" of Gaza ranks "among the worst assaults on any civilian population in our time and age".
The BBC has seen evidence of rape, sexual violence and mutilation of women during the 7 October Hamas attacks.
The Hamas attack on southern Israel on 7 October killed 1,200 people, with around 240 others taken hostage.
Hamas officials in Gaza say at least 16,248 people have been killed in Israel's retaliatory campaign, including about 7,000 children.
