Mr. Renzi is making the issue central to his own Facebook posts and a conference he will kick off in Florence on Friday evening to call attention to the issue.
This week, government officials publicly denounced pictures on websites supportive of the Five Star Movement, a web-savvy anti-establishment party, that falsely captioned a government minister’s appearance at a funeral to make it seem as though she were mourning Salvatore Riina, the murderous Mafia boss.
Another video showed Mr. Renzi, a former prime minister who is waging an uphill battle to return to power, at a years-old news conference with President V. Vladimir Putin of Russia. A false translation of Mr. Putin’s Russian made it seem as if he were blaming the Italian government for the national soccer team’s failure to qualify for the World Cup this month.
Andrea Stroppa, a researcher with a company called Ghost Data who advises Mr. Renzi on cybersecurity issues, contributed to a report about fake news that Buzzfeed published this week and that has become one of Mr. Renzi’s chief talking points. After the report was published, Facebook shut down the sites, which trafficked in nationalistic and anti-immigrant screeds.
Davide Colono, a member of the family that managed the sites, said the content was merely intended to attract clicks in a country fed up with the Democratic Party’s government. He called the shuttering of the sites “against the freedom of the press” and “just politics.”
Facebook representatives have told Italian officials that they are planning to dispatch an Italian “task force” of fact-checkers to address the fake-news problem here before the elections, according to a government official who was present during the negotiations but was not authorized to speak on the record.
Facebook declined to comment on Friday about those plans.
Mr. Stroppa has also prepared a report for Mr. Renzi that attempts to demonstrate a connection between seemingly unrelated sites promoting rival anti-establishment political movements critical of Mr. Renzi and the center-left government.
The report, which Mr. Stroppa shared with The New York Times, shows that the official web page of a movement promoting Matteo Salvini, leader of the far-right League party, shares unique Google codes with a fan and propaganda page supportive of the Five Star Movement.
The codes, used to track advertising and web traffic, are also shared by an array of other sites, some of which spread wild conspiracy theories, attack Mr. Renzi or deliver explicitly pro-Russian spin.
One site, IoStoConPutin.info, or I’m With Putin, excoriates the United States investigation of Russian involvement in the American election as “fake news” and features posts written by anonymous staff, including one with the headline “Putin Model of a Real Leader,” which features the reporting of Sputnik Italia.
Another, mondolibero.org, peddles a distinctly anti-American and anti-liberal worldview. “Moscow Reveals That Twitter Relies on the U.S. Secret Services,” one headline read.
The assorted sites share a unique ID assigned by Google Analytics to keep track of how a site is performing, as well as an AdSense number through which Google manages advertisements placed on the sites, according to data in Mr. Stroppa’s report and verified by The Times.
All the sites also share a template on their contact pages. But in the murky world of internet propaganda and subterfuge, the tilt of the content is clearer than where it originates, and what the shared codes amount to is not entirely clear.
“We frequently see unrelated sites using the same IDs, so that’s not a reliable indicator that two sites are connected,” said a Google spokeswoman, Simona Panseri.
Some analysts, however, noted that the ad revenues would flow to the same operator and suggested that the assigning of separate site ID numbers indicated the hand of a single manager, who could then easily track traffic and metrics.
Google would not identify the site administrators. Emails sent to addresses listed on the contact pages of the sites went unanswered.
Chris Norton, a spokesman for Facebook, said, “We take the issue of fake news incredibly seriously.” And he added that the company considered the issue of accurate information on the platform “especially important during elections.”
He said it was disrupting the economic incentives for false news, removing fake accounts and investing in resources and technology to address the problem. But Facebook declined to identify the administrator of the accounts with the shared Google codes.
A spokesman for the Five Star Movement said the fan page in question that shared the codes was not an official site and could have been made by an independent activist.
Asked about the shared codes between his official web page and the page promoting the Five Star Movement, Francesco Zicchieri, a leader of the “We’re With Salvini” movement, appeared legitimately bewildered.
“I don’t even know what we are talking about,” he said, adding that the party’s web guru, Luca Morisi “does everything” for the movement’s assorted sites.
Late Friday evening Mr. Morisi acknowledged that the site We’re With Salvini shared the same Google codes as sites outside the League’s political universe. He explained that a former supporter of the Five Star Movement had helped build the We’re With Salvini site and pasted codes from his Five Star fan page, as well as I’m With Putin and his conspiracy sites, onto the official page.
“But we have nothing to do with the pro-Putin or pro-Five Star sites,” Mr. Morisi said, explaining that he thought he had actually changed the codes in the past and promised to do so this weekend to clear up any confusion.
The League and the Five Star Movement are not nominally allied, and even cast themselves as rivals. But they share an interest in advancing the pro-Russia, anti-establishment and anti-immigrant agenda that has made Five Star the most popular party in Italy.
Five Star says it has sworn off any coalition alliances, but Mr. Salvini recently indicated that he would be open to forming a coalition.
This month, “The Kremlin’s Trojan Horses 2.0,” a study by the Atlantic Council, an American think tank, put Mr. Salvini’s party and the Five Star Movement in the “pro-Russian camp,” in part for their opposition or skepticism toward the European Union and NATO.
Mr. Salvini’s party signed a cooperation agreement in March 2017 with Mr. Putin’s United Russia Party, and Mr. Salvini, who uses xenophobic and anti-Muslim language, has repeatedly praised Mr. Putin as an ally against Islamic terrorism.
The Five Star Movement has hosted on its associated websites anti-Renzi propaganda originating on Russian outlets such as Sputnik or RT.
“We are at a crossroads,” said Mr. Renzi, who, for now, stopped short of pointing a finger directly at Russia for interference in Italy’s coming election, which he cast as a choice between growth and instability.
The former prime minister said he had no proof of Russian involvement, and worried that raising the specter of Mr. Putin could become a reason “to not do anything” when Facebook now has the ability to close pages infected by apparently homegrown fake news.
“It’s not enough to evoke the Russian danger,” he said, “when there is proof in our hands.”