In the first attack in a Jewish settlement in the West Bank city of Hebron, a Palestinian attempted to stab an Israeli civilian, the Israeli military said. The Israeli, who was carrying a gun, shot and killed the attacker.
Shortly after, Israeli border police stopped to question a Palestinian man walking in "a suspicious manner" through a neighborhood around East Jerusalem, a police spokesman said. The man drew a knife and tried to stab the officers, who shot him dead, the spokesman said.
No Israeli was hurt in the incidents.
Two weeks of violence has been triggered in part by Palestinians' anger over what they see as increased Jewish encroachment on Jerusalem's al-Aqsa mosque compound, which is also revered by Jews as the location of two destroyed biblical Jewish temples.
Israel says it is keeping the status quo at the holy compound.
The unrest has claimed the lives of 39 Palestinians, including knife-wielding assailants, as well as children and protesters shot by Israeli forces during rock-throwing confrontations.
Seven Israelis have been killed in random attacks in the street or on buses.
The United States has stepped up efforts to try to restore calm to the region. Secretary of State John Kerry spoke by phone with both Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas to discuss ways to end the violence.
Kerry and Netanyahu will meet next week in Germany.
Palestinians want East Jerusalem, annexed by Israel in a move not recognized internationally, as the capital of a state they aspire to establish in the West Bank and Gaza Strip. Israel regards all of Jerusalem as its indivisible capital. Peace talks collapsed in 2014.
