Twitter has responded to this hack through their official support handle informing users that they are currently working to stop this attack.
“We are aware of a security incident impacting accounts on Twitter. We are investigating and taking steps to fix it. We will update everyone shortly.
You may be unable to Tweet or reset your password while we review and address this incident. We’re continuing to limit the ability to Tweet, reset your password, and some other account functionalities while we look into this. Thanks for your patience.”

They went further to say investigation is ongoing. And assured users that most accounts should be able to Tweet again. As they continue working on a fix, this functionality may come and go.
“We detected what we believe to be a coordinated social engineering attack by people who successfully targeted some of our employees with access to internal systems and tools.
We know they used this access to take control of many highly-visible (including verified) accounts and Tweet on their behalf. We’re looking into what other malicious activity they may have conducted or information they may have accessed and will share more here as we have it.”
Twitter has locked accounts that were compromised and will restore access to the original account owner only when they are certain it is secure.