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Twitter said users whose security was compromised will be receiving an email with instructions to create a new password.
"Your old password will not work when you try to log in to Twitter," said Bob Lord, Twitter's director of security.
Twitter also advised that users do not use the same password more than once across other services and accounts.
Twitter's director of information security, Bob Lord said the hacking attack on the social networking site "was not the work of amateurs".
In its statement to users, Twitter said that it reset the pilfered passwords which had been hacked and sent users emails advising them that they will have to create a new one.
Twitter noted a recent surge in security breaches at several U.S. media and technology companies.
The New York Times and The Wall Street Journal reported this week that their computer systems had been infiltrated by China-based hackers.
Twitter says hackers may have gained access to information on around 250,000 of its more than 200 million active users.
Twitter has issued a message to reassure its users after the social networking site detected "unusual access patterns" that led to "unauthorized access attempts to Twitter user data".
In a statement on Twitter's blog it said that its investigation had detected that attackers may have had access to usernames, email addresses and passwords for around 250,000 users.
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250,000 Twitter users have had their accounts hacked after the social networking site revealed its security had been breached.