Gugino's lawyer has since called the president's accusations "dark, dangerous, and untrue."
"No one from law enforcement has even suggested anything otherwise so we are at a loss to understand why the President of the United States would make such dark dangerous, and untrue accusations against him," Kelly Zarcone said in a statement of the president's accusation against her client, who she said has been released from the ICU but remains hospitalized.
Tagging the conservative news outlet OANN (One America News Network), the president said in his tweet "I watched, he fell harder than was pushed. Was aiming scanner. Could be a set up?"
In response, former Vice president Joe Biden on Tuesday afternoon called both the officers' actions and Trump's comments an "abuse of power," adding the president's suggestion is "a conspiracy theory he saw on TV."
"My Dad used to say there's no greater sin than the abuse of power. Whether it's an officer bloodying a peaceful protester or a President defending him with a conspiracy theory he saw on TV. I'm a Catholic – just like Martin. Our faith says that we can't accept either," Biden tweeted, around the same time his video message for Floyd's funeral was played.
Republican Sen. Lisa Murkowski of Alaska, who said last week she has struggled with whether she could back Trump, prompting the president to threaten to campaign against her in a tweet, when asked for her reaction to Trump's tweet, said, "This is not good."
"I just saw that this second. It just makes no sense that we're fanning the flames right at this time," she told reporters on Capitol Hill. "This is not good."
New York Gov. Andrew Cuomo, a Democrat, responding to the president's tweet at a news conference Tuesday, said, "How reckless, how irresponsible, how mean, how crude."
"There's no fact to any of it." Cuomo said. "What do you think, it was staged? You think that the blood coming out of his head was staged? Is that what you are saying? You saw his head hit the pavement, and you see blood on the pavement."
Video of the incident shows Gugino walking in the direction of a crowd of uniformed officers when two officers appear to shove him. He then falls onto his back and the back of his head hits the concrete. The sound of the Gugino's head hitting the ground silenced the crowd, the video shows. Blood can be seen seeping from Gugino's head as he laid motionless as several officers walk by him, before another officer, possibly a National Guard member, came to his aid.
The two Buffalo police officers seen pushing Gugino in the video are now facing criminal charges in connection with the incident, prosecutors said over the weekend, after a spokesperson for the city and police department, Mike DeGeorge, initially said in a statement that the man "tripped and fell."
Officers Aaron Torgalski and Robert McCabe were charged with second-degree assault during their video arraignments on Saturday and were released on their own recognizance. They both entered not guilty pleas and are expected back in court on July 20.
Cuomo said at a news conference on Saturday that the video was "horrendous, disgusting" and said he believed it to be illegal. "A bad police officer is an enemy of every good police officer," Cuomo said.
No officials have suggested what the president alleges, that Gugino was acting as anything other than a peaceful demonstrator or that he was acting as part of a "set up."
The president's own chief of staff, Mark Meadows, declined to comment on Trump's tweet when reporters asked him about it Tuesday afternoon. Earlier, the White House had also declined to comment and said it had no information to offer beyond what Trump shared on Twitter.
"I learned a long time ago not to comment on tweets and I'm not going break that right now," Meadows said.
All 57 members of the Buffalo Police Department's Emergency Response Team resigned Friday from the unit in an apparent show of support for two officers who were suspended after the incident was filmed Thursday night.
The president's tweet comes on the heels of a roundtable meeting with law enforcement representatives on Monday in which Trump said the panel would discuss policing and "talk about ideas how we can do it better and how we can do it, if possible, in a much more gentle fashion."
"Sometimes, you'll see some horrible things like we witnessed recently, but 99 -- I say 99.9, but let's go with 99% of them are great, great people, and they've done jobs that are record setting -- record setting," Trump said, referring to Floyd's death.
ABC News' Ben Gittleson and Molly Nagle contributed to this report.
This report was featured in the Wednesday, June 10, 2020, episode of “Start Here,” ABC News’ daily news podcast.
"Start Here" offers a straightforward look at the day's top stories in 20 minutes. Listen for free every weekday on Apple Podcasts, Google Podcasts, Spotify, the ABC News app or wherever you get your podcasts.