A panel of ministers approved the legislation yesterday and it will now be taken up by the country's parliament.
Government watchdogs have expressed concern such a law could be abused and harm free speech.
The legislation, known as the "Facebook bill" in Israel, would allow the government to petition a court to have online material it considers incitement removed.
It would be removed in cases where it poses "a real risk to the security of a person, the public or the state," Justice Minister Ayelet Shaked said in a statement.
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In September, Shaked said that the social network giant had removed 95 percent of the posts Israel had referred to it.
Shaked said Sunday that in 2016, 71 percent of the 1,755 requests Israel filed to internet companies requesting they remove content were fully complied with.
She noted the ongoing collaboration with the internet companies, but stressed that it was "important this cooperation will be obligatory".
Public Security Minister Gilad Erdan, who also pushed for the bill, accused Facebook and other internet companies of not removing "inciting content" every time police ask them, or not doing so swiftly enough "despite the fact that incitement leads to terror."
But the possibility for error was seen in September, when Facebook apologised after temporarily disabling accounts linked to two Palestinian news sites critical of Israel.
The move drew concern over the potential for online censorship.
The Israel Democracy Institute think-tank said the bill was "unprecedented" in its current form when compared to similar legislation in other countries.
It said it would be difficult to enforce and would "facilitate a disproportionate amount of censorship."
Palestinians say they fear the Israeli campaign will lead to censorship of legitimate information and suspect the closures in September were linked to it.