Nitsana Darshan-Leitner, director of the Shurat HaDin organisation that filed the lawsuit in the New York State Court on Monday, said the claim holds the Internet giant responsible for the presence of posts that incite violence.
It calls on the company to remove over 1,000 inflammatory pages and improve its monitoring mechanisms, but does not seek monetary damages.
"The same way they can tell what coffee you drink in the morning and push you ads or connect me with my friends that have similar hobbies, they can monitor these threats and take down the posts of encouragement and glorification of terror attacks," Darshan-Leitner told AFP.
Around 20,000 Israelis have backed the move in an online petition, but are not plaintiffs in the case, added the activist lawyer, whose group files legal actions it says are aimed at safeguarding Jewish rights.
"This lawsuit is without merit and we will defend ourselves vigorously," Facebook said in a statement to AFP.
"We want people to feel safe when using Facebook. There is no place for content encouraging violence, direct threats, terrorism or hate speech on Facebook," the statement said.
"We urge people to use our reporting tools if they find content that they believe violates our standards so we can investigate and take swift action."
Darshan-Leitner said that "so far, people complaining about hate speech or incitement on Facebook could not prove that these incitements led (directly to) an imminent and realistic danger."
Nine Israelis have been killed in a series of stabbing attacks and shootings since October 1, while dozens have been wounded.
Fifty-six Palestinians and one Israeli Arab have been killed in the same period, around half of whom are alleged attackers.
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With no political movement appearing to spearhead the unrest, social media posts praising the attacks and encouraging them have been accused of stoking the violence.
One video, highlighted by Israel's ambassador to the UN, included a section showing the best spots on the body to stab someone in order to kill them.
The hashtag "#Jerusalemintifada" in Arabic has been widely shared online and videos of attacks and their aftermath are quickly uploaded.
Israeli Prime Minister Benjamin Netanyahu has characterised the uprising as "Bin Laden meets (Facebook founder) Mark Zuckerberg."
Facebook has 30 days to respond to the claim.
Darshan-Leitner said that success would open up other social media, including Twitter and YouTube, to similar lawsuits.
A channel allegedly affiliated with militant Islamist group Hamas was removed from YouTube earlier this month after a complaint from the Israeli foreign ministry.
In February, in a case also brought by Shurat HaDin, an American court found the Palestine Liberation Organisation and the Palestinian Authority liable for six attacks in Jerusalem that killed 33 people and wounded more than 390 others between January 2002 and January 2004.
They were ordered to pay more than $650 million (580 million) in damages to the families of American victims and are appealing the lawsuit.