In the first incident, a Palestinian with a knife allegedly tried to stab an Israeli civilian near the Gush Etzion settlement bloc, south of Jerusalem, but was shot dead by soldiers at the scene, she said.
A civilian passerby was lightly injured.
Another Palestinian attempted to attack an officer with a pickaxe at a crossing point in the northeastern West Bank, but was shot dead by a bullet to the head by the officer, the spokeswoman said.
The attacker was a 19-year-old woman, the official Palestinian Wafa news agency reported.
More than 100 Palestinians have been killed in an ongoing wave of violence since October 1, according the Palestinian health ministry.
Israel says the vast majority were shot dead after being implicated in violence, which has included 82 knife attacks and attempted knife attacks, 30 shootings and 12 car rammings.
Others were shot dead in clashes with Israeli security forces.
Eighteen Israelis have been killed in the attacks. An Eritrean – mistaken by a security guard and by bystanders for an assailant, a Palestinian bystander, mistaken by an attacker for a Jewish Israeli, as well as a US national were also killed.
Also on Tuesday, An Israeli court handed a 36-month jail sentence to a Jewish extremist who torched a mixed Jewish-Arab school in Jerusalem last year, according to a court document sent to dpa by the Jerusalem District Court.
Yitzhak Gabai, in his early 20s and from a West Bank settlement near Jerusalem, was the third person to be convicted and sentenced in the December 2014 arson attack.