The new round of violence came ahead of Israeli Prime Minister Benjamin Netanyahu's trip to Washington, where he will meet US President Barack Obama on Monday.
Attacks and violent protests throughout October raised fears of a new Palestinian uprising, but violence had waned in recent days. Unrest has often erupted after the main weekly Muslim prayers on Fridays.
Most of the recent violence has occurred in the southern West Bank city of Hebron and have mainly involved stabbings.
Medics said the victims were a 16-year-old in serious condition and a lightly wounded 18-year-old.
The incident occurred at the site known to Jews as the Tomb of the Patriarchs and Muslims as the Ibrahimi Mosque, and the army said around 4,000 Jewish worshippers were visiting Friday as part of a religious pilgrimage.
Hebron has 200,000 Palestinian residents with approximately 500 Israeli settlers living in the centre, protected by an army-patrolled buffer zone. The situation is a constant source of tensions.
The shootings followed a string of incidents earlier in the day.
In the first, an elderly Palestinian woman was accused of attempting to ram Israeli soldiers with a car in Hebron and was shot dead by troops, the Israeli army said.
Palestinian medics said the alleged assailant was 72-year-old Sharwat Sharawi, adding that she was driving in pouring rain at the time. They alleged she did not intend to attack the soldiers.
Later in the Gaza Strip, 23-year-old Salame Abu Jamaa was shot dead by Israeli security forces in clashes near the border with Israel, the enclave's health ministry said.
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