Draft laws proposed today would bring in fines of up to €50m (£44m) for the companies failing to delete such content online flagged by users.
Fresh tests of the platforms' abilities to take down content that was reported as illegal, found too few posts were taken down and that the ones that were, were not taken down quickly enough, said justice minister Heiko Maas.
"The biggest problem is that the networks do not take the complaints of their own users seriously enough," he said, adding that it will increase pressure on the companies to get results.
"It is now clear that we must increase the pressure on social networks. We need legal regulations to make companies even more obligated to eradicate criminal offenses."
Google video site YouTube was commended for improving its performance, with a 90 per cent deletion rate of posts reported, 82 per cent of them within 24 hours. For Facebook, that stood at 33 per cent within the first 24 hours, seven percentage points lower than previous tests, while just one in 100 Tweets containing criminal content was erased and that did not happen within 24 hours.
"There can be just as little space in the social networks as on the street for criminal muttering and slander. Facebook and Twitter have not used the opportunity to improve their deletion practices. Too few punishable comments are deleted," said Maas.
In addition to fines for failure to comply, the draft law proposes that social networks make clear the means of reporting such content to users, that complaints be looked at immediately in the context of its legality and if breaking the law, be deleted within 24 hours, as well as informing users of the decision in regard to a complaint.
Facebook, Twitter and Google were among tech companies to sign up to an EU code of conduct last summer, designed tackle hate speech in light of terror attacks in Europe. But, they were warned in December by Brussels that they need to act faster, noting collectively that just 40 per cent of cases were dealt with in the 24 hour time frame they are aiming for.