The president slammed his predecessor for his role in the violence on 6 January without mentioning him by name, only referring to him as the “defeated former president”.
The South Carolina senator, one of Mr Trump’s staunchest allies, tweeted: “What brazen politicization of January 6 by President Biden.”
“I wonder if the Taliban who now rule Afghanistan with al-Qaeda elements present, contrary to President Biden’s beliefs, are allowing this speech to be carried?” he added.
The senator’s comments were in stark contrast to his words on the day that pro-Trump rioters stormed the US Capitol on 6 January.
When the Senate sat again later that day, he remarked: “Trump and I, we’ve had a hell of a journey. I hate it to end this way. Oh my God, I hate it. From my point of view, he’s been a consequential president, but today, first thing you’ll see. All I can say is count me out. Enough is enough.”
On January 7, 2021, he also said: “When it comes to accountability the president needs to understand that his actions were the problem, not the solution.”
In later tweets on Thursday morning, Mr Graham expressed continued outrage that the Capitol was breached in the first place and paid tribute to law enforcement personnel who risked their lives to protect congress.
He then accused President Biden and Vice President Kamala Harris of using the anniversary of a “dark day in American history” as an effort to “resurrect a failed presidency”.
Republican Senate Minority Leader Mitch McConnell released a statement similarly acknowledging that: “January 6th, 2021 was a dark day for Congress and our country,” but continuing: “it has been stunning to see some Washington Democrats try to exploit this anniversary to advance partisan policy goals that long predated this event.”
Florida Governor Ron De Santis was similarly dismissive in remarks to reporters in Palm Beach on Thursday morning, likening the commemoration of the day to a “nauseating” media circus and saying that he didn’t expect anything good to come out of what “Pelosi and the gang are doing”.
He then touted a conspiracy theory that the FBI was involved in orchestrating the insurrection at the Capitol.
Representatives Matt Gaetz and Marjorie Taylor Greene made an appearance on Steve Bannon’s War Room podcast on Thursday morning and were defiant with their take on the events of the day.
Mr Gaetz said: “We’re ashamed of nothing. We’re proud of the work we did on January 6 … and we’re actually going to walk the grounds that patriotic Americans walked from the White House to the Capitol.”
Fox News presenter Laura Ingraham was dismissive about President Biden’s speech, tweeting: “Someone might want to tell Biden that Trump’s no longer president.”
Mr Biden used the phrase “former president” 16 times in his speech and didn’t mention his name once.
Ms Ingraham also tweeted: “Of course, Biden’s lame speechwriter couldn’t resist a dig at the Founding Fathers — ‘as imperfect as they were.’”