SAN FRANCISCO — Twitter said on Tuesday that it would continue to be lenient with world leaders who appeared to violate its policies against violent speech because the company believed preserving those tweets served the public interest.

The announcement came as Twitter grapples with scrutiny for hosting President Trump’s increasingly virulent messages about the impeachment proceedings against him.

[Times Investigates: In Trump’s Twitter feed: Racists, conspiracy-mongers and spies.]

Under pressure from Democrats to take action against Mr. Trump’s account, Twitter said that it would take action against a world leader’s account only if it was used to threaten an individual, promote terrorism or self-harm, or post private information like a phone number.

“The accounts of world leaders are not above our policies entirely,” the company said in a blog post. “Presently, direct interactions with fellow public figures, comments on political issues of the day, or foreign policy saber-rattling on economic or military issues are generally not in violation of the Twitter Rules.”