Twitter has hidden tweets from Donald Trump and the official White House account for "glorifying violence".
In his post, the US president quipped "when the looting starts, the shooting starts" amid violent protests in Minneapolis following the death of an unarmed black man in police custody.
Twitter said the message violated its "rules about glorifying violence" but the post would remain accessible and not be deleted entirely as it may be in the public's interest.
Mr Trump's tweet was then reposted word-for-word by the White House account, which Twitter also hid.
Another post from the White House account said "the president did not glorify violence. He clearly condemned it" and accused Twitter of having "biased, bad-faith 'fact-checkers'".
The 46-year-old died on Monday after police officer Derek Chauvin knelt on his neck while he was handcuffed and lying face-down on the road.
He could be heard repeatedly saying "please" and "I can't breathe" to the officer, who kept his knee on his neck for almost eight minutes - including after Mr Floyd had become unresponsive.
In his first mention of the incident, the president blamed the protests on "a total lack of leadership" in Minneapolis, directing a tweet towards who he described as "the very weak radical left mayor, Jacob Frey".
Mr Trump also suggested he could "send in the National Guard and get the job done right", before then making the comment about shooting unarmed looters.
The full tweet that Twitter has censored reads: "...These THUGS are dishonoring the memory of George Floyd, and I won't let that happen. Just spoke to Governor Tim Walz and told him that the Military is with him all the way.
"Any difficulty and we will assume control but, when the looting starts, the shooting starts. Thank you!"
Users must now bypass a message from Twitter to read Mr Trump's tweet.
The message says: "This Tweet violated the Twitter Rules about glorifying violence. However, Twitter has determined that it may be in the public's interest for the Tweet to remain accessible."
Twitter's decision is the latest indication that the company will no longer give high-profile users free reign over their comments on the platform.
Earlier this week, Twitter labelled another of the president's tweets about allegedly fraudulent mail-in ballots with a fact-check warning.
The president subsequently accused the company - and the entire social media industry - of censorship and anti-conservative bias, before signing an executive order aimed at curbing protections for the sites as publishers.
Professor Orin Kerr at the University of California, Berkeley, accused Mr Trump of being ignorant of constitutional law with his actions, both in terms of targeting Twitter and his threat to the demonstrators.
He said the targeting of unarmed looters with lethal force was in contravention of the fourth amendment, and that the move to curtail protections for social media platforms was in contravention of the first amendment.