In a statement aimed at clarifying its policies, Twitter said it reserves the right to take "enforcement action" on offending tweets, notably those including threats of violence or posting of private information.
The move comes with social media, and Facebook, in particular, facing pressure over enabling false and misleading statements from political leaders.
Both Facebook and Twitter have said they would not attempt to remove "newsworthy" comments from political leaders, and Facebook has exempted political ads from fact-checking.
Twitter said its policy does not give free rein to policial figures.
"We want to make it clear today that the accounts of world leaders are not above our policies entirely," the company said in a blog post.
Twitter said it would take action against any account for "promotion of terrorism" or "clear and direct threats of violence" as well as the inclusion of private information, such as a home address or phone number.
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It would also act on the posting of intimate photos or videos of someone without consent, and any post related to child sexual exploitation or promoting self-harm.
Twitter said it has not changed its policy which gives leeway to political speech.
The policy announced in June exempts most political commentary from its rules.
It previously indicated that if a tweet from a world leader violates Twitter's rules but there is a "clear public interest" in the information it may require users to click on a notice acknowledging they want to see the message.
"Our goal is to enforce our rules judiciously and impartially," Twitter said.
"With critical elections and shifting political dynamics around the world, we recognise that we're operating in an increasingly complex and polarised political culture. These are constantly evolving challenges and we'll keep our policies and approach under advisement."
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Facebook has notably been slammed for allowing President Donald Trump to run ads which critics say included debunked information on Democratic candidate Joe Biden.
Another Democratic hopeful, Senator Elizabeth Warren, stepped up her battle with Facebook by running her own ad with deliberately false information, stating: "Mark Zuckerberg and Facebook just endorsed Donald Trump for re-election."
Facebook noted that similar to broadcasters, it does not seek to censor political messages.
"We agree it's better to let voters -- not companies -- decide," Facebook said in response to Warren.
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