Palestinian kills US tourist in Israel
The American, named as Taylor Force, was one of 10 people stabbed by an attacker in Jaffa, south of Tel Aviv.
US Vice-President Joe Biden was at an event close by at the time.
Earlier, two Israeli police officers were shot and wounded in occupied East Jerusalem. An ultra-Orthodox Jew was stabbed in Petah Tikva, near Tel Aviv.
Israeli police said the attackers in all three incidents were Palestinian, and had been killed.
Wave of attacks
Israeli police said the attacker in Jaffa stabbed a number of people in the port area, before moving through the city attacking others.
The Magen David Adom ambulance service said five of the wounded were in a serious condition.
The American stabbed to death has been identified as a student at Vanderbilt University in Nashville, Tennessee.
Taylor Force was on a trip to Israel to learn more about global entrepreneurship and start-ups, university chancellor Nicholas Zeppos told his fellow students in a letter.
Others on the trip were safe and unharmed, Zeppos said, calling the incident a "horrific act of violence".
Biden, who had been attending an event with former Israeli President Shimon Peres in the nearby Peres Centre for Peace at the time, "condemned in the strongest possible terms the brutal attack" and "expressed his sorrow at the tragic loss of American life", the White House said in a statement.
Israeli police said the attacker was a 21-year-old from the West Bank town of Qalqilya who was shot dead at the scene.
In the Jerusalem attack, police said a gunman opened fire on a group of police officers outside the Old City's Damascus Gate, seriously wounding one of them. The suspect wounded another in the subsequent chase, but was then shot and killed, police said.
Meanwhile, witnesses in the Tel Aviv suburb of Petah Tikva said a Palestinian attacker was killed with his own knife by the ultra-Orthodox Jew who he had just stabbed. The wounded man was rushed to hospital to be treated for wounds to his upper body.
At least 29 Israelis have been killed in a wave of stabbing, shooting or car-ramming attacks by Palestinians or Israeli Arabs since October.
More than 180 Palestinians - mostly attackers, Israel says - have also been killed in that period.
The assailants who have been killed have been shot dead either by their victims or by security forces as they carried out attacks. Some attackers have been arrested.
Other Palestinians have been killed in clashes with Israeli troops.