PostGhost, a website that records the tweets of influential people even after they're deleted, is shutting down after receiving a cease and desists notice from Twitter.

The site archived the posts of verified users with more than 10,000 followers. PostGhost was only a few days old before Twitter threatened to shut down its API for showing deleted Tweets, which violates the platform's developer tool policies.

PostGhost agreed to shutter the site but argued it was providing a public service and that influential public figures should be held accountable for what they say on Twitter.

"We created the website postghost.com to provide the public with a more accurate history of public statements made by the most influential public figures on Twitter," wrote PostGhost's creators.

"When a public figure makes a public statement in the real world, be it in print, in person, or on their own website, writers, bloggers and individuals have the right to reprint and discuss that statement at will, even if the speaker wishes he or she could take it back. As Twitter becomes the default worldwide platform for online speech, losing that right is a loss for public discourse as a whole."

The incident isn't the first time that a service that records deleted tweets has been forcibly shut down. Politwoops, a network of sites that saves the Tweets politicians delete, was closed by Twitter last year. It was later reinstated following an outcry from advocacy groups including the Electronic Frontier Foundation and Human Rights Watch.

PostGhost's admins admitted that not all users should have their deleted tweets stored; its verified user criteria covers just 0.05 percent of all Twitter account holders. "We believe that for such prominent verified Twitter users, the public has a right to see their public Twitter history, whether or not they grow to regret the statements they've made," it said.

Whether PostGhost eventually returns in some limited capacity remains to be seen. The site said it is "happy to continue a dialogue" with Twitter as it attempts to find a compromise.