UK watchdog Ofcom is set to gain the power to block access to online services that fail to do enough to protect children and other users.
The regulator would also be able to fine Facebook and other tech giants billions of pounds, and require them to publish an audit of efforts to tackle posts that are harmful but not illegal.
The government is to include the measures in its Online Harms Bill.
The proposed law would not introduce criminal prosecutions, however.
Nor would it target online scams and other types of internet fraud.
This will disappoint campaigners, who had called for the inclusion of both.