Israeli forces have launched a ground offensive on the northern Gaza city of Jabalia, while continuing attacks in the southern city of Rafah. Israel's military says the Islamic group Hamas is trying to regroup in Jabalia.
The Israeli military said on Sunday that its ground troops killed 10 Hamas fighters during the attacks in Rafah.
More than one million displaced people are sheltering in Rafah.
The United Nations estimates that about 300,000 people have evacuated from Rafah. The UN is calling for a halt to the fighting, saying that there is no safe place in the Gaza Strip.
The Israeli military earlier said it had seized control of Jabalia. But it has announced the launch of a ground operation there following airstrikes. The military stressed that it had urged residents in the area to evacuate.
Qatar-based satellite news network Al Jazeera has broadcast images of people fleeing from bombardments, including elderly citizens and children, and injured people being transferred for medical treatment.
Israeli Prime Minister Benjamin Netanyahu met people who are expected to take part in a ceremony scheduled for Tuesday to commemorate the country's independence.
He said, "We will defeat our enemies; we have no other choices."