Residents of the southern Israeli city of Ashkelon have been told to head to safe rooms after reports of more militants crossing from Gaza - following rocket fire earlier.
US President Joe Biden has described Hamas' assault on Israel - launched on Saturday - as an "act of sheer evil".
Details of a massacre in an Israeli village where fighting continued until Tuesday morning have emerged - with an Israeli general speaking of babies killed in their bedrooms.
Israeli soldiers also told BBC International Editor Jeremy Bowen that some of the dead had been beheaded.
Almost four days after Hamas began its unprecedented assault on its enemy, the Israeli military has continued to bomb Gaza - killing two high-ranking Hamas officials.
The death toll in Israel has reached 1,200, while more than 900 people have been killed in Gaza.
Israel says there's been another exchange of fire across its border with Lebanon, and that it's also responded in kind after shells were fired from Syria.