The police also recommended that charges of fraud and breach of trust be brought against Netanyahu and his wife.
In this long-running scandal, Mr Netanyahu is suspected of passing regulations favouring the Bezeq telecommunications firm in exchange for favourable coverage on the Walla news website, which is owned by Bezeq's controlling shareholder.
Police have already recommended indicting Netanyahu on corruption charges in two other cases.
Netanyahu's manipulation of Walla! has been widely reported by local media, but last week a fuller expose on Israel's Channel 10 featured both former and present employees of the news site describing in detail how stories were changed or completely removed if they did not flatter the Prime Minister and his wife.
In Case 1000, Netanyahu is suspected of having received gifts from businessmen overseas totaling 1 million shekels (approximately $280,000), including cigars, champagne, jewelry and more, from 2007 through 2016. In return, the police said, Mr. Netanyahu, who personally oversaw the communications ministry from 2014 to 2017, rewarded Bezeq with enormously lucrative concessions, including approval of its merger with Yes, a satellite television company, despite the objections of lower-level ministry officials.
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Fast-forward another year, to December 2, 2018, and those two incidents, the original attempt to allegedly obstruct, and, a year later, Yeshua's coming clean to investigators, form the backbone of a police recommendation document that may be the most serious threat to Netanyahu's political future thus far.
Mr Netanyahu did not mention the allegations in his comments at the start of a cabinet meeting later in the day.
"A prime minister with so many corruption cases around him can not continue at his job and must resign", Gabbay tweeted. The attorney general will make the final decision on whether to press charges.
Opposition leader Avi Gabbay, chairman of the Zionist Union party, called for the Prime Minister to stand down immediately.
"He'll send a message to the attorney general that everyone knew about these three police reports and they still voted for him and want him in power", Hazan said. "There was no fraud, no breach of trust or any other felony". "A person with such a sickly obsession with what the media says about him must not lead the State of Israel".
Mr Netanyahu held the government's communications portfolio until a year ago and oversaw regulation in the field.