Five Palestinians have been killed and several wounded by Israeli soldiers near the West Bank town of Nablus. Palestinians say another man was killed when Israeli combat helicopters fired on his car in the Gaza Strip.
Israeli and Palestinian officials are giving conflicting accounts of pre-dawn events near Nablus.
Nablus Governor Mahmoud Aloul says Palestinian civilians were killed as they tried to rescue a gunman who was fatally wounded by soldiers during a firefight.
An Israeli army spokeswoman says the Palestinians were killed in a gunfight after an elite commando unit spotted a group of militants planting a bomb in an area under Israeli control.
In the Gaza Strip, Palestinians say a member of the Palestinian security services was killed when Israeli helicopter gun ships fired missiles at his car.
Earlier in Gaza, the Israeli military fired missiles at a Palestinian police station near Khan Yunis, destroying the building. An army spokeswoman said that assault was in response to Palestinian mortar attacks on Jewish settlements in Gaza.
In Rafah, in the southern Gaza Strip, Palestinians say a man was shot in the chest and killed. Palestinians say the shooting was not preceded by fighting in the area.
As the violence raged, both Israeli and Palestinian leaders responded positively to a German initiative to host cease-fire talks.
German Foreign Minister Joschka Fischer, on a diplomatic mission to the region, has been trying to arrange a meeting between Palestinian leader Yasser Arafat and Israeli Foreign Minister Shimon Peres to discuss ways to end the violence. "This meeting should be well prepared," Mr. Fischer said. "I think the United States, the Europeans, and also the Russian friends, altogether we are discussing the issue. We are all together on the same line. I think the unity of the international community is very important. It is a big chance for both parties."
Mr. Peres is reportedly ready to propose a gradual truce that is to begin in quieter areas of the Palestinian territories. In return, Israel would ease travel restrictions for Palestinians who live in those areas.
But political analysts are expressing little optimism there would be a breakthrough if such a meeting takes place.