Typically, prominent people, including musicians, journalists and company executives, get a blue icon on their profile after proving their identity.
However, some far-right and white-supremacist accounts have now also been verified.
Twitter founder Jack Dorsey said the scheme would now be "reconsidered".
In a statement, the company said: "Verification was meant to authenticate identity and voice, but it is interpreted as an endorsement or an indicator of importance.
"We recognise that we have created this confusion and need to resolve it."