A number of high-profile US figures - including the likes of Bill Gates, Joe Biden and Elon Musk - were hit in an apparent Bitcoin scam earlier this month and Twitter has now revealed that a number of DMs (Direct Messages) were also accessed.
The company did not reveal whose private messages were compromised but it did admitted that one was owned by an elected official in the Netherlands.
Dutch far-right politician Geert Wilders told the BBC that this was a reference to his Twitter account but the company has not confirmed this.
He said: "I was informed by Twitter last night... that my Twitter account was not only hacked for some days and the hacker also posted tweets on my account and sent DMs in my name, but indeed also got full access to my DMs, which of course is totally unacceptable in many ways.
"People critical of Islam or regimes in the Middle East [including those] from within countries like Iran, Saudi Arabia and Syria [have sent me DMs over 10 years] and I do hope they will not be in danger if their identity would be exposed because of this hack.
"I had deleted most of them but maybe some were left there for the hacker to see and copy."
In a statement, the FBI - which is investigating - said "the accounts appear to have been compromised" with the goal of cryptocurrency fraud, as they urged the public to remain vigilant.