The comments from GPO head Nitzan Chen come in the wake of a CBS News story about an attack at the Damascus gate entrance of the Old City of Jerusalem that killed one police officer and injured a second.
Three Palestinians carried out a shooting and stabbing attack, killing Border Police officer Hadar Cohen and injuring another officer. The Palestinian attackers were shot dead at the scene.
In its report about the attack, CBS published the headline: "Three Palestinians killed as daily violence grinds on."
"This time we will not let it pass quietly," Chen posted on Facebook. "We are considering rescinding press passes from journalists and editors who are negligent in their work and present headlines that flip the reality."
The Israeli Foreign Ministry denounced the headline as, "outrageous, biased and incorrect."
Amid pressure from Israeli officials, CBS changed the headline to: "Palestinians kill Israeli officer, wound another before being killed."
In October, Chen issued a similar warning to the BBC over its coverage of a deadly attack in Jerusalem that killed two and injured three, including a toddler.
An attacker fatally stabbed a man and wounded his wife. The couple's 2-year-old son was also hurt in the attack, while a man who rushed to help the family also was killed. The attacker opened fire on police, who shot him dead.
The BBC ran a story about the attack with the headline: "Palestinian shot dead after Jerusalem attack kills two."
Following outrage from Israelis, the BBC changed its headline to: "Jerusalem: Palestinian kills two Israelis in Old City."
— RoNy KaTz (@RonyKatz) January 26, 2016
At the time, Chen called the initial headline "outrageous," and said there is "a limit to the lack of objectivity in press coverage."
"While the BBC corrected its title … I intend to reprimand the head of their office in Israel and to warn him directly that we do not intend to let this pass unchallenged," he added.