Twitter, which was originally invented as a text message-based network before it evolved into a Web-based multimedia platform, allows users to still access stripped down versions of its service.
(Read more: Silent no more, El-Erian takes to Twitter)
Following his speech, Erdogan's office said in a statement that Erdogan was referring to what it called Twitter's failure to implement Turkish court orders seeking the removal of some links and that they may be left with no option but to ban the platform.
"If Twitter officials insist on not implementing court orders and rules of law ... there will be no other option but to prevent access to Twitter to help satisfy our citizens' grievances," the statement said.
Thursday's apparent blocking was only the latest clash between Turkey's ruling party and social media companies including Google, Facebook and Twitter.
(Read more: Erdogan says Turkey could ban Facebook and YouTube)
After a series of popular protests partly fueled by Twitter last summer, Erdogan slammed the service as "a scourge." Shortly thereafter a government minister asked Twitter to establish an office in the country so that it could better communicate requests to take down content or hold the company accountable to Turkish law. Twitter did not respond to the request.
Erdogan said two weeks ago that Turkey could also ban Facebook and YouTube, which he says have been abused by his enemies after a stream of audio recordings purportedly revealing corruption in his inner circle emerged online.