Her appeal comes in the wake of the killing of Al Jazeera correspondent Shireen Abu Akleh, who was shot dead on Wednesday when she covered an Israeli raid in Jenin in the West Bank.
The Palestinian-American veteran was buried in East Jerusalem on Friday and large crowds turned up for her funeral.
“shocking” use of force
The High Commissioner made a statement saying that she “followed with deep concern” the events in the occupied West Bank, including East Jerusalem.
“Pictures of Israeli police attacking mourners at journalist Shireen Abu Akleh’s funeral procession in East Jerusalem on Friday, May 13, were shocking. Reports indicate that at least 33 people were injured,” she said.
Ms Bachelet said Israeli use of forcewhich was filmed and broadcast live, seemed unnecessary and must be investigated quickly and openly.
“There must be responsibility for the horrific killing not only of Shireen Abu Akleh but for all the killing and serious damage in the Occupied Palestinian Territory,” she said.
Call for inquiries
The UN High Commissioner for Human Rights reported that 48 Palestinians have been killed by Israeli security forces so far this year.
The latest death occurred on Saturday when a young man named Walid al-Sharif succumbed to injuries he sustained during clashes last month at the Al Aqsa Mosque in Jerusalem.
“As I have called for many times before, there must be appropriate investigations into the actions of the Israeli security forces, “said Bachelet.
“Anyone found responsible should be brought to justice with criminal and disciplinary sanctions commensurate with the seriousness of the offense. This culture of impunity must end now.”
The Security Council’s condemnation
The assassination of Abu Akleh has sent shock waves around the world, and UN officials have been among those calling for an investigation.
The journalist was shot despite wearing a vest that identified her as a member of the press corps. Her producer was also injured.
U.N Safety advice made a statement on Friday strongly condemning her killing and reiterating that journalists should be protected as civilians.
The Council also called for an immediate, thorough, open and fair and impartial inquiry into her killing, and stressed the need to ensure accountability.