Israel's military bombarded southern Gaza's main city in what it said was the heaviest fighting, while the United States again pressed to allow fuel and vital aid into the Palestinian enclave.
The surge in combat comes after a truce between Israel and Hamas collapsed last week.
Hamas' armed wing said it killed or wounded eight Israeli troops and destroyed 24 military vehicles on Tuesday.
Gaza health officials said many civilians were killed in an Israeli strike on houses in Deir al-Balah, north of Khan Younis.
Dr Eyad Al-Jabri, head of the Shuhada Al-Aqsa Hospital there, told Reuters at least 45 people were killed.
The US aid chief on Tuesday announced new support for the war-battered Gaza Strip on a visit to Egypt, as a renewed Israeli offensive again puts Palestinians at risk.
Samantha Power, the administrator of the US Agency for International Development, traveled to the Egyptian town of El-Arish, the gateway to Rafah, the border crossing that has been reopened but at limited capacity since the war started.
Power announced $21 million in new US assistance that will include hygiene and shelter supplies and food for people in Gaza, where water and other basics have been in short supply.
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