Gaza City - traditionally a Hamas stronghold - was surrounded, military spokesperson Rear Admiral Daniel Hagari said.
The Israeli military said its troops and tanks were encountering mines and booby traps as they advanced in Gaza.
Those who live in Gaza City and the north will have to find shelter elsewhere as the Israeli forces have cut off roads.
Israeli spokesperson Hagari said Israeli was also "highly prepared" on its northern border with Lebanon, where he said Iranian-backed militants were carrying out actions with the aim of diverting it from the war in Gaza.
Palestinians trapped in Gaza City hoped that a truce could be reached soon.
Persons:
Daniel Hagari, Leo Varadkar, Antony Blinken, Benjamin Netanyahu, Israel, Mustafa Dalul, Khan Younis, Amir Cohen, Ayman Safadi, Safadi, Abu Ubaida, Gazans, Hagari, Nidal al, Ali Sawafta, Dan Williams, Emily Rose, Maytaal, Clauda, Patricia Zengerle, Phil Stewart, Idrees Ali, Michael Perry, Angus MacSwan, Miral Fahmy, Andrew Cawthorne
Organizations:
Ireland's, Palestinian, Palestine, United, Israel, REUTERS, Jordan's, Qatari, West Bank, Workers, Reuters, Thomson
Locations:
Gaza, Israel, GAZA, JERUSALEM, Gaza City, Blinken, Iran, United Arab Emirates, Amman, United States, Egypt, Rafah, Lebanon, Iranian, Ramallah, Jerusalem, Dubai, Washington