If passed into law as now appears likely, the measure would compel large outlets such as Facebook and Twitter to rapidly remove fake news that incites hate, as well as other "criminal" content, or face fines as high as 50 million euros ($53 million).
Germany's justice minister said hate speech posed a grave danger to harmonious living in a free, open and democratic society.
Already, a few fake news reports have emerged in Germany, including one falsely alleging a rape previous year of a German girl of Russian descent by asylum seekers.
German Justice Minister Heiko Maas said the companies are responsible for policing and removing hateful content from their sites and that "there is no room for criminal incitement on social media".
Google was judged to have faired better at swiftly nixing hate speech from its social sharing platform YouTube.
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Beyond hate speech and fake news, the draft legislation also covers other illegal content, including child pornography and terrorism- related activity.
The companies would have 24 hours to remove any posts that openly flout German law after they are flagged by users.
But critics warned that the proposed law could stifle freedom of expression.
She also said that the hefty fines envisaged in the bill would work as "almost an invitation to not only delete real insults, but everything for safety's sake".
Facebook said it was examining the proposed rule, but stressed that it has heavily invested in boosting the resources of its content review team. "That would have a serious impact on free speech on the internet", Bernhard Rohleder, manager of Bitkom, a German group representing 2,400 digital companies, said in a statement.
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The new law would give social networks 24 hours to delete or block criminal content and seven days to deal with less clear-cut cases, with an obligation to report back to the person who filed the complaint about how it was handled.
Mr Maas acknowledged that freedom of expression "has huge significance in our democracy".
"In the end, we need European solutions for companies that operate across Europe", Mr Maas told reporters.
Stephen Deadman, Facebook's global deputy chief privacy officer, said at a conference in Berlin last month that the social media giant's scale makes it hard to monitor and filter everything that gets published and that it had hundreds of staff working on the issue.
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