U.S. Republican senators have chosen to stay silent or dodge over responses to a Tuesday tweet by President Donald Trump saying that a 75-year-old man may have staged his fall after he was shoved by police during a demonstration against the police killing of George Floyd.

Trump said on the social media platform that Martin Gugino, the man involved in the incident last week, "could be an ANTIFA provocateur," a reference to the collective of anti-fascist activists who usually adopt violence when protesting.

"I watched, he fell harder than was pushed," the U.S. president said without giving further evidence backing his claim.

The video footage of the incident went viral. The elderly man was severely injured in the head after falling to the ground and it can be seen from the video footage that the blood was coming out around his head. Gugino is currently still recovering in the hospital.

At a press briefing on Tuesday following the weekly Republican policy lunch, Senate Majority Leader Mitch McConnell wouldn't comment on Trump's tweet and circumvented the question when asked by reporters. "As I said, we are discussing in the Senate Republican conference what response we think is appropriate to the events of the last two weeks."  

Other senators also refused to comment on whether Trump's tweet was appropriate when they were asked by reporters on Capitol Hill. Some of them simply said they were not aware of the tweet, according to CNN.

Sen. Marco Rubio of Florida said, "I didn't see it, you're telling me about it. I don't read Twitter, I only write on it."

Sen. John Cornyn of Texas said, "You know a lot of this stuff just goes over my head," explaining that he didn't see the tweet. 

However, the Republican president's tweet on the protester still triggered a  backlash among other senators as well as the condemnation from Democrats. 

Sen. Mitt Romney of Utah said, "I saw the tweets, it was a shocking thing to say, and I won't dignify with any further comment."

Sen. Lisa Murkowski of Alaska, who is considered as a moderate, said that "it just makes no sense that we are fanning the flames right at this time, this is not good."

At a press conference on Tuesday, Governor of New York State Andrew Cuomo slams Trump for making such groundless statements.

"You saw his head hit the pavement. You see blood on the pavement. Maybe he fell harder than he was pushed," the Democratic governor said. "How reckless, how irresponsible, how mean, how crude."

Senate Minority Leader Chuck Schumer from the Democratic Party also criticized Republicans' silence on the issue.

"Republicans have been ducking and dodging about this. Leader McConnell was asked about it. He didn't say anything, when a 75-year-old man is pushed to the floor and he's bleeding… They can't even speak about that," Schumer said.

(Cover: U.S. Senate Majority Leader Mitch McConnell faces reporters following the Senate Republicans weekly policy lunch on Capitol Hill in Washington, June 9, 2020.)