Justice Minister Heiko Maas says the German government could take legal action against Facebook and other social media groups if they do not intensify their fight against illegal hate speech or Islamist "terror phantasies".
On Monday, Mr Maas said Facebook, Twitter and Google, are removing illegal content from the internet more frequently and quickly, but more work was needed.
He said the social media groups responded mostly to requests by government-funded organisations but did not take private complaints as seriously.
"Of the illegal content reported by users, Twitter deletes about one per cent, YouTube just 10 per cent, and Facebook about 46 per cent,"
Mr Maas said those rates were too low.
The Justice Minister said he would decide on next steps after government study was completed in March, could not rule out legal measures.
"The situation has improved, but it's not nearly good enough… We have to keep up the pressure on the companies."
German political leaders and regulators say Facebook, the world's largest social network, with 1.6 billion monthly users, has been slow to respond to hate speech and anti-immigrant messages.
European Union Commissioner Vera Jourova told the news conference with Mr Maas that she was counting on voluntary steps by social media firms and preferred to avoid deadlines.
Mathias Doepfner, who heads Germany's Axel Springer media group, told newspaper executives that media organisations should be regulated like telecommunications firms, which are "not held responsible if people use their phone to talk about stupid or dangerous stuff".
Facebook touched off a firestorm earlier this month when it deleted an iconic Vietnam War photo of a naked girl fleeing a napalm attack, saying it violated restrictions on nudity.
The company later reinstated the photograph after it received multiple complaints, including from Norwegian Prime Minister Erna Solberg, who accused Facebook of censorship and of editing history.