The number of Palestinian militants killed in the latest violence at the start of the Jewish Passover holiday rose to 13 while 16 Israeli soldiers were reported injured, according to reports on Sunday.
At least six militants were killed in an Israeli missile attack on the northern Gaza Strip Saturday.
Three militants from the Islamist Hamas movement were killed in one of the heaviest bomb attacks on a border crossing in the Strip since Israel's withdrawal in the summer of 2005.
An Israeli army spokeswoman said 16 Israeli soldiers were injured, one seriously, in the attack on the Kerem Shalom border crossing in the southern Gaza Strip.
A spokesman for Hamas' military wing, al-Qassam Brigades, said the militants had used three booby-trapped cars, detonating two in the attack.
The Israeli army said the attack was followed by another at the southern border crossing of Kissufim.
General Yoav Galant, in charge of the Israel's southern command, said the clashes were the fiercest since Israel's withdrawal from the Gaza Strip in the summer of 2005.
He added that the attacks on Kerem Shalom and Kissufim were well synchronized and designed to kill as many Israeli soldiers as possible as well as capture soldiers.
Hamas movement claimed responsibility for the attack, saying the aim of its Operation Warning before the Explosion was to break the Israeli blockage on the territory that has been in place since Hamas came to power in Gaza since mid-June 2007.
The latest violence comes after Israel sealed off all Palestinian territories for about a week due to the Passover holiday, when Jews mark the exodus of Jews from Egypt in ancient times.