At least 30 people, including children, were killed in an Israeli air strike on a United Nations-run school in the Gaza Strip, according to Palestinian medical sources.
Many Palestinian families across Gaza have fled their homes for UN-run schools and shelters, as Israel's military operation in Gaza reached its 11th day.
Israeli forces earlier refocused attacks in the Gaza Strip to include the southern town of Khan Younis.
Hamas and Islamic Jihad said their fighters had engaged Israeli soldiers with machine-guns and rockets in Gaza City, where residents reported loud explosions and heavy gunfire.
Plumes of smoke rose above the territory as Israeli infantry, supported by helicopters and tanks, clashed with Hamas militants.
Four Israeli soldiers were killed by fire from one of their own tanks in northern Gaza early on Tuesday, while at least 70 Palestinians were reportedly killed.
Relatives of an Israeli soldier killed in the Gaza Strip on Monday mourned his loss at his funeral in Jerusalem.
Elsewhere in Jerusalem, Israelis prayed for the well-being of troops fighting in Gaza.
Later, Palestinians in the West Bank city of Ramallah took part in a candlelit vigil in support of Gaza.
Protests against Israel's military offensive continue in many countries around the world, including Syria, where images of Israeli leaders were burnt.
Palestinian medical officials say at least 110 people have died since the ground assault began on Saturday, while Israel says it has killed 130 Hamas fighters.
Aid agencies in Gaza speak of appalling conditions for treating casualties of the continuing Israeli bombardments.