Anyone caught repeatedly viewing ISIS videos online faces a jail term of 15 years, the Home Secretary has announced.
The move will strengthen the existing offence of possessing information likely to be useful to a terrorist so it does not only apply to downloaded or stored information.
Academics, journalists and other professionals would have a “reasonable excuse” defence for legitimate work.
The maximum penalty will also apply to terrorists who publish information about members of the armed forces, police and intelligence services to fuel attacks.
Home Office analysis found that over the last 12 months, Islamic State supporters have published almost 67,000 tweets in English promoting its propaganda.
Ms Rudd said: “I want to make sure those who view despicable terrorist content online including jihadi websites, far right propaganda and bomb making instructions face the full force of the law.
“There is currently a gap in the law around material which is viewed or streamed from the internet without being permanently downloaded.
“This is an increasingly common means by which material is accessed online for criminal purposes, and is a particularly prevalent means of viewing extremist material such as videos and web pages.”
She added: “Changes will enable police and the security service to keep pace with modern patterns of internet use and intervene earlier in an investigation given the speed with which online radicalisation is taking place.
“It is also right that the cowardly targeting of the men and women who serve our country is punished in the severest terms.
“We are continuing to urgently press the internet companies to do more to stop this kind of vile material being available on their platforms in the first place.”