Combat aircraft, artillery and drones are said to have been used in the attacks.
The Israeli military's tanks have also been spotted in Gaza City, according to reports in Palestinian media, writes The Jerusalem Post.
Over 320,000 Palestinians have so far left Gaza City and moved to other parts of Gaza, estimates the Israeli military. Alone during the night towards Monday, around 20,000 are estimated to have left the city, writes The Times of Israel.
Israeli military urged last week to evacuate the entire city ahead of a planned offensive against Hamas in the area.
Civilians have been urged to go to an area described by Israel as a humanitarian zone, but many residents believe that nowhere in Gaza is safe.