The so-called "recommendations bill" would end the police's current practice of recommending to prosecutors whether to indict suspects upon completing their investigations.
It also aims to stem leaks from the investigations themselves, stating that no police recommendations be made public and penalising those found leaking to the media.
The bill has been pushed by Netanyahu's staunchest allies in the Likud Party, whipping up criticism that the beleaguered prime minister himself was seeking to pass legislation that would in essence change the current rules for police investigations and protect him from embarrassing revelations they may have discovered.
He said he asked a lawmaker behind the bill to ensure that it "be worded in a way that it won't apply to the investigation taking place into my affairs."
Also Read
Organisers hope the grassroots movement picks up steam and becomes a regular Saturday night ritual that eventually forces Netanyahu from power.
Earlier today, Israeli police questioned a close Netanyahu ally seen as the driving force behind the bill on separate corruption charges.
Coalition whip David Bitan was grilled in relation to accusations that he promoted the interests of criminals in return for debt relief while he was a municipal politician years ago.
The bill's future remains unclear. Netanyahu's Likud party was set to bring the bill for a parliamentary vote tomorrow, but appeared to be lacking support and working to delay the vote.
Netanyahu has been questioned in two cases and police say they suspect him of being involved in bribery, fraud and breach of trust.
Police have already grilled him six times regarding gifts he received from Hollywood and business figures, and in another probe about secret talks with the publisher of a major Israeli newspaper in which Netanyahu allegedly requested positive coverage in exchange for reining in a free pro- Netanyahu daily. One of his closest former aides has become a state's witness against him.
Another investigation has engulfed his close associates and dominated news in Israel. The probe relates to a possible conflict of interest involving a $2 billion purchase of German submarines.
Netanyahu's personal attorney, who is also his cousin, represented the German firm involved and is suspected of trading his influence over the prime minister in return for a hefty cut of the deal.
A former Cabinet minister and top former navy and security officials have been questioned by police. Netanyahu has yet to be named a suspect in that probe.
Disclaimer: No Business Standard Journalist was involved in creation of this content