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Social media companies in Germany face fines of up to 50m euros ($57.1; £43.9m) if they fail to remove "obviously illegal" content in time.
From October, Facebook, YouTube, and other sites with more that two million users in Germany must take down posts containing hate speech or other criminal material within 24 hours.
Content that is not obviously unlawful must be assessed within seven days.
The new law is one of the toughest of its kind in the world.
Failure to comply will result in a 5m euro penalty, which could rise to 50m euros depending on the severity of the offence.
On Fake news:
Mr Maas, who oversaw the legislation, told the German parliament that online hate crimes had increased by almost 300% in the past few years, adding that "no one should be above the law".
The bill was drafted after several high-profile incidents of fake news and criminal hate speech being spread on social media sites in Germany.
One case involved the targeting of prominent Green MP Renate Kunast, with a post that falsely suggested she was sympathetic to a refugee who had murdered a German student in the southern city of Freiburg.
http://www.bbc.com/news/technology-40444354