The company has apologised.
Twitter has admitted that some users tweets were made public after a bug in the system. It applied to people who had their accounts private for more than four years. The bug meant that the users' posts were made public even though they chose to keep them private.
The company said in a statement: "We recognise and appreciate the trust you place in us, and are committed to earning that trust every day.
"We're very sorry this happened and we're conducting a full review to help prevent this from happening again."
The bug occurred on accounts between November 2014 and January 2019. Affected users have been notified, however Twitter is urging everyone using the site to review their account's privacy settings.
The company's chief executive Jack Dorsey told a US committee: "In the spirit of accountability and transparency: recently we failed our intended impartiality."
He also promised that the issue has since been fixed.
