The social-networking site – where people post very short, constant updates – allows Internet users to track what others are doing. Though the 140-character "tweets" often deal in the mundane, they have also helped break news and organize protests, from anticapitalist rallies in London to a cross-country democracy march in Pakistan.
Access to Twitter became unusually difficult Tuesday afternoon.
The apparent shutdown follows a number of other steps that officials have taken ahead of June 4.
On Saturday, former Tianananmen prisoner Wu Gaoxing was detained. He had written an open letter to President Hu Jintao seeking compensation for people imprisoned after the 1989 crackdown. Other dissidents have also been put under house arrest or close surveillance.
In recent years, access to YouTube, Western media outlets, and myriad other websites has also been blocked, often before or after sensitive events.
But in the ongoing cat-and-mouse game between censors and citizens, Internet users quickly alerted one another to the news about Twitter via chatrooms.