An Israeli politician says the country is considering sending soldiers into the Gaza strip, an area of land lived in by Palestinians.
More than 400 people have been killed since Israel began air strikes which they say are targeted at places linked to the Palestinian group, called Hamas, last Saturday.
Four people have been killed by rockets fired into Israel from Gaza.
Both sides have ignored calls from world leaders to stop the fighting.
On Friday, thousands of Palestinians in the West Bank demonstrated against the attacks.
Smoke rising after an air strike in Gaza
Protests have also been held in other places around the world, including in the Indonesian capital Jakarta, and Sydney in Australia, plus cities in Kenya and Iran.
Hamas is the leading political group in Gaza, after it won elections there in 2006.
The group has a big military section, which has a history of carrying out violent attacks against Israel.
On Thursday, one of its top leaders, Nizar Rayan, died when his home got hit by a bomb.
Israel says it is attacking Gaza because militants from Hamas have been firing rockets into Israel recently, and it wants that to end.
It says a large number of its troops and tanks are gathered on the Gaza border.