Seven Palestinians - at least five of them militants - have been killed by Israeli troops.
Palestinian boys gathered around the car in Jenin after the shooting
Two of the dead breached the tightly guarded northern Gaza Strip border and were in Israel when they were shot.
In the West Bank city of Jenin, three militants were killed. One of the dead is thought to be a leader of the militant group Islamic Jihad.
Palestinian officials said two teenage boys were also killed by Israeli troops in an unrelated incident in Gaza.
Medical officials said the two were civilians aged 15 and 16, who were shot close to an Israeli observation post near the town of Beit Lahiya.
Troops were sent to the Erez border crossing after two gunmen scaled an eight metre (25ft) wall using a ladder, the Israeli military said.
In an ensuing gun battle, at least one Israeli soldier was lightly wounded and the Palestinians were killed.
The militants were 700m into Israeli territory when they were killed, the Associated Press news agency quoted the Israeli army's Maj Tal Lev-Ram as saying.
The two dead men were on a "martyrdom operation" against Israel, a spokesman for a Palestinian militant group said.
The Gaza clash was confirmed in statements by spokesmen for some of the smaller Palestinian militant groups, and it appears that the gunmen came from different groups.
The militants claimed that three gunmen had breached the Gaza border, but the Israeli army said there were only two.
In Jenin, Israeli forces said they killed three Palestinian militants when they opened fire on a car.
According to army officials, the three militants had two assault rifles and ammunition in the car.
Israeli troops have killed at least 20 Palestinians in the last week.
The army says the operations are needed to protect Israeli civilians from attacks.