Twitter said it was a co-ordinated attack targeting its employees with access to internal systems and tools.
The company said in a series of tweets that the hackers used the access to take control of many highly-visible including verified accounts and Tweet on their behalf.
It added that “significant steps” were taken to limit access to such internal systems and tools while the company’s investigation was ongoing.
Meanwhile, Twitter chief executive Jack Dorsey tweeted that it was a tough day for Twitter.
One cyber-security expert said that the breach could have been a lot worse in other circumstances.
Twitter earlier had to take the extraordinary step of stopping many verified accounts marked with blue ticks from tweeting altogether.
Password reset requests were also being denied and some other “account functions” disabled.