Germany's tough new social media law was meant to rid Twitter and Facebook of hateful and illegal content. But critics say that at just 96 hours old it is already choking press freedom.

The debate flared up after Twitter (TWTR) blocked the account of German satirical magazine Titanic on Wednesday. The publication posted tweets that parodied a far-right politician whose social media accounts were blocked earlier this week because of anti-Muslim posts.

Among others, Titanic parodied a tweet by Beatrix von Storch, deputy parliamentary leader of far-right party, Alternative for Germany (AfD), in which she accused police of appeasing what she called "barbaric, gang-raping Muslim hordes of men."

Von Storch's account was suspended by Twitter on Monday, as were those of other AfD politicians who posted similar tweets in support of her.

Police have accused von Storch and AfD parliamentary leader Alice Weidel of inciting hatred and prosecutors are investigating. Von Storch has since deleted some of the tweets, and her account has been restored.

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Titanic's editor in chief Tim Wolff said in a statement he was "shocked" by Twitter's decision to block the magazine's account. The monthly magazine has a circulation of 100,000, and has been published since 1979.

The publication is not afraid of controversy. It was sued by the Catholic Church in 2012 over its portrayal of the Pope. It also once sent offers of "bribes," including cuckoo clocks and ham, to world soccer's governing body, FIFA.

Under the new law, which took full effect in Germany on Monday, Twitter, Facebook (FB) and other social media companies can be fined as much as €50 million ($60 million) if they fail to remove hate speech and fake news posts quickly.

Companies now have 24 hours to remove posts that breach German law after they are flagged by users. The law came into force in October, but the government gave companies three months to adjust to the new rules.

Freedom of speech activists have warned that the steep fines could lead to companies blocking legitimate content -- such as the satirical tweet by Titanic.

Asked about Titanic, a Twitter spokesman said the company does not comment on individual accounts because of privacy and security concerns.

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The German Federation of Journalists, which has criticized the law since it was first proposed last year, described Twitter's move against Titanic as an attack on the freedom of the press.

Federation chairman Frank Uberall said the suspension of Titanic was exactly the kind of censorship the group has warned about for months, and he called for the law to be scrapped.

"A private company based in the U.S. is deciding the extent of freedom of the press and opinion in Germany. That's a sell-out of our fundamental rights," he said in a statement.

German officials defended the law, which they said brings rules covering hate speech and illegal content on digital platforms into line with those already imposed on print media.

Justice minister Heiko Maas said that "freedom of expression is not a license to commit crimes."

"Anyone who distributes criminal content online must be held accountable," he told German newspaper Bild on Wednesday.

Germany has tougher hate speech laws than many other countries. Free speech rights are enshrined in the country's constitution, but hate speech, Holocaust denial and display of certain symbols, such as the swastika, are illegal and punishable by prison.