"We absolutely do work with law enforcement on issues like these," Del Harvey, Twitter's senior director of trust and safety, told the BBC's "Newsnight" program. "These sorts of threats are against the rules. We suspend accounts when they're reported to us. We're working to make it easier to report those accounts. We think this is really important."
Some say Twitter can't, and shouldn't, police the Internet. While the U.S. Supreme Court has ruled that First Amendment protections of freedom of speech apply to the Internet, restrictions on online expression in other Western democracies vary widely.
In Germany, where it is an offense to deny the Holocaust, a neo-Nazi group has had its Twitter account blocked. In Britain, hundreds of people are charged each year for sending menacing, indecent, offensive or obscene messages. People have been convicted for making offensive comments about a murdered child and for posting on Facebook that soldiers "should die and go to hell."
Some civil libertarians are wary of criminalizing even more online activity.
They argue that most online talk is just that — talk, never intended to translate into action. GQ magazine recently reprinted some of the blood-curdling threats it received from One Direction fans after running a cover story on the boy band that some fans found insufficiently reverential. Many of the comments were obscene, intemperate and violent — but few people suggest the tweeters should be prosecuted.
Padraig Reidy of civil liberties group Index on Censorship cautioned that the "report abuse" button was no quick fix — it could itself be abused by governments to silence their opponents or by celebrities to muzzle their critics.
He said stopping "real harassment, threats and incitement" would involve cooperation by Twitter, police, prosecutors and users of social networking sites.
"We often think that just because things are happening online there is a technical solution to make the Web a better place," Reidy said. "But it's going to take real engagement."
Anti-trolling campaigners have already taken matters into their own hands — retweeting abuse in order to expose the problem to the light.
A group of women in Britain has coined the #everydaysexism hashtag to chronicle the extent of misogyny many women still face. Last month it was used to draw attention to dozens of tweets calling Wimbledon women's tennis champion Marion Bartoli "fat," ''ugly," a "slut" and even more offensive terms.
Sometimes such "naming and shaming" can be remarkably effective.
This week a Twitter troll sent an abusive and sexually explicit tweet to Mary Beard, a Cambridge University classicist and television presenter. Beard retweeted it to her 43,000 followers, and soon a second Twitter user was offering to supply the mailing address of the offender's mother so she could see what her son had written.
He quickly became contrite. "I was wrong and very rude," he wrote. "Hope this can be forgotten and forgiven."
Jill Lawless can be reached at http://Twitter.com/JillLawless