The social networking site will start removing tweets that break local laws. But it says no message will be taken down until an internal review determines there's a legal problem.
Twitter insists its commitment to free speech remains firm.
San Francisco-based Twitter, founded in 2006, depicted the new system as a step forward. Previously, when Twitter erased a tweet, it vanished throughout the world. Under the new policy, a tweet breaking a law in one country can be taken down there and still be seen elsewhere.
"This is a good thing for freedom of expression, transparency and accountability," said Twitter's general counsel. "This launch is about us keeping content up whenever we can and to be extremely transparent with the world when we don't. I would hope people realize our philosophy hasn't changed."
There have been calls though, in a barrage of tweets, to boycott the site until the censorship initiative is scrapped.
The Associated Press contributed to this story.