Three Palestinian militants have been shot dead by Israeli troops in the West Bank, local officials have said.
The funeral of a Palestinian policeman killed near Jenin
Two members of the al-Aqsa Martyrs' Brigades and one Islamic Jihad member were killed when their car was fired on in the city of Jenin, the sources said.
Israel confirmed an undercover unit had fired on the car and hit three men.
Hours later, Palestinian militants in the Gaza Strip fired three rockets at the southern Israeli town of Sderot, one of them hitting a house.
Two people were taken to hospital with light wounds, medical sources told AFP news agency. Four other people were treated for shock at the site,
In other violence, a Palestinian policeman was shot dead by Israeli troops near Jenin, Palestinian sources said.
And in Gaza, masked gunmen detonated explosives at the American International School in Gaza but no-one was hurt.
The two members of the al-Aqsa Martyrs' Brigades who died in Jenin were named as Abbas al-Damaj and Ahmad Ayassa.
Saeb Erekat, a key aide to Palestinian Authority President Mahmoud Abbas, condemned the violence.
Militants attacked the private school in Gaza before dawn
"This undermines our efforts to bring about a cessation of hostilities. As such, I believe this is very, very bad," he said.
Israel and Palestinian militants have observed a truce since November, although Israel has launched some raids, and militants in Gaza have fired some rockets into Israel.
The policeman who died, Mohammed Abed, was watching an Israeli operation in the village of Kafr Dan from a roof when he was shot, Palestinian security forces said.
The Israeli army said its soldiers had been under attack during the operation and had fired on a man armed with a rifle.
In the Gaza school attack, the explosives were detonated before the start of school, when the buildings were empty.
Several security guards at the site were overpowered but were not harmed by the attackers.
The school is part of an association of American schools in the Middle East, but US embassy officials say it has no connection with the US government.
The militants also stole computers and other equipment before making their escape