The new rule would apply on accounts belonging to political figures, verified users and verified accounts with more than 100,000 followers.
The harmful tweets would, however, won't be deleted.
"That said, there are cases, such as direct threats of violence or calls to commit violence against an individual, that are unlikely to be considered in the public interest," Twitter Safety said in a blog post on Thursday.
The notice a screen you have to click or tap through before you see the tweet to provide additional context and clarity will be immediately visible in your home timeline and across other areas like search.
A light gray box will appear before the tweet, notifying users that it's in violation, but it will remain available to them.
"In the past, we've allowed certain tweets that violated our rules to remain on Twitter because they were in the public's interest, but it wasn't clear when and how we made those determinations," said the micro-blogging platform.
A cross-functional team including Trust and Safety, Legal, Public Policy and regional teams will determine if the tweets are a matter of public interest based on the criteria.
"In instances where a tweet violates our rules and our review doesn't find that it would be in the public interest to leave it up, we will require the account owner to remove the Tweet. Either way, this notice will make our decision-making clearer," said the company.
When a tweet has a notice placed on it, it will feature less prominently on Twitter and will not appear in "Safe" search, "Timeline", "Live" events pages, "Recommended Tweet" push notifications, "Notifications" tab and "Explore" tab.
"This notice won't be applied to any Tweets sent before today and it's unlikely you'll encounter it often. We cannot predict the first time it will be used, but we wanted to give you more information about this new notice before you come across it on Twitter," explained the company.
( With inputs from IANS )