Israeli forces shot dead a Palestinian in the West Bank on Friday and Palestinian militants in Gaza fired a rocket into the Jewish state, despite a partial truce declared by armed groups in the territory.
An Israeli army spokesman said a Palestinian man threw a petrol bomb at Israeli border police manning a security roadblock in the West Bank city of Hebron, lightly wounding one of the officers.
Israeli forces shot at him and killed him.
Palestinian hospital officials confirmed the man's death. His family said he had gone out early to pray at a local mosque and that he did not belong to a militant group.
The army spokesman said the man was found to have been carrying a knife.
Citing security concerns, Israel maintains a network of roadblocks in the territory that restricts Palestinian travel between West Bank cities.
Palestinians and many foreign nations and human rights groups accuse Israel of collective punishment.
Also on Friday, a rocket fired by Palestinian militants in Gaza landed in southern Israel, said the Israeli army and witnesses quoted by Israeli media.
There were no reports of casualties or an immediate claim of responsibility.
Palestinian militant groups had earlier in the week said they would halt such attacks if Israel stopped targeting Palestinians in the West Bank and Gaza.
After their declaration, Israel ended a massive five-month-long offensive in Gaza.
Israel had begun its assault, billed mainly as an attempt to stop the almost-daily rocket strikes, after armed Palestinian groups in Gaza, including the governing Hamas faction, abducted an Israeli soldier in a raid inside the Jewish state in June.
The United States Secretary of State Condoleezza Rice, visiting the region to try to revive long-stalled peace talks, pushed Israelis and Palestinians on Thursday to broaden their fragile Gaza ceasefire.
The Palestinians have also been bogged down by internal disputes and some violence, mainly over unpaid government salaries, after Western nations froze funding to the Palestinian Authority after Hamas won a parliamentary election in January.
Early on Friday, unknown assailants detonated explosives at the entrance to a Gaza branch of the Arab Bank, causing damage to a part of the building, Palestinian security sources said.
The motive for the bombing, the first against a foreign-operated bank in the Palestinian territories, was unclear and there was no claim of responsibility.
Talks between Hamas and President Mahmoud Abbas's Fatah group to establish a unity Palestinian government, which the West says must renounce violence and recognise Israel and past peace deals with the Jewish state, remain deadlocked.