Kirk, 31, the co-founder of right-wing group Turning Point, was fatally shot as he spoke at a university event in Utah.
"This is a dark day for our state. It's a tragic day for our nation," said Utah Governor Spencer Cox. "I want to be very clear this is a political assassination."
There is no suspect in custody after hours of confused statements from US officials, and a manhunt for the shooter is ongoing. Earlier, two people were arrested, and later released.
Video footages shows Kirk addressing students at an outdoor event when a single shot rings out and he can be seen reaching up his neck. Stunned spectators are heard gasping and screaming before people start to run away.
"It is long past time for all Americans and the media to confront the fact that violence and murder are the tragic consequence of demonising those with whom you disagree day after day, year after year, in the most hateful and despicable way possible," Trump said in a video address.
"For years, those on the radical left have compared wonderful Americans like Charlie to Nazis and the world's worst mass murderers and criminals," the president said.
"This kind of rhetoric is directly responsible for the terrorism that we're seeing in our country today, and it must stop right now."
Trump went on to list some high-profile instances of violence, including an assassination attempt on his own life during his presidential campaign in which he was slightly injured at a rally in Pennsylvania, the killing of a health executive in New York last year and the 2017 shooting of House majority leader Steve Scalise as he blamed "radical left political violence."
He did not mention political violence against Democratic politicians, such as the fatal shooting of Democratic state representative Melissa Hortman and her husband in June or the 2011 Tucson shooting in which six people were killed and Gabby Giffords, a Democrat representing Arizona, was seriously hurt.
Kirk was a powerful force in grassroots conservative politics, leading youth organisation Turning Point USA, hosting a popular podcast and attracting millions of followers on social media.
The killing has been denounced by political allies and foes alike in the US and across the world, with condemnation coming from previous presidents Bill Clinton, George Bush, Barack Obama, Joe Biden and overseas leaders including Israel's Benjamin Netanyahu and the UK's Sir Keir Starmer.
But even amid the bipartisan expression of grief and shock, the political divisions in the US were writ large.
What was meant to be a moment of silence in the US House of Representatives erupted into shouting and finger-pointing.
Some Democrats questioned why other killings that involved less prominent figures were not getting the same attention, according to one lawmaker present, which resulted in swearing and accusations about politicising tragedies.
Republican House Speaker Mike Johnson pounded the gavel for order, while an unidentified person shouted, "Pass a gun law!"
According to the most recent data compiled by the Centres for Disease Control and Prevention, 46,728 people died from gun violence in the US in 2023, the third-highest figure ever recorded.
Before the identity of the shooter was known, prominent right-wing figures were framing the incident as a part of a broader assault by the left against conservatism
"America has lost one of its greatest champions," White House Deputy Chief of Staff Stephen Miller wrote on X. "All of us must now dedicate ourselves to defeating the evil that stole Charlie from this world."
Elon Musk, the X platform's billionaire owner, was even more blunt. "The Left is the party of murder," he wrote.
Trump - who routinely refers to his political rivals as "radical left lunatics" representing an existential threat to America - called the shooting an outgrowth of overheated rhetoric.
The reaction from Democrats was more muted. "We don't yet know what motivated the person who shot and killed Charlie Kirk, but this kind of despicable violence has no place in our democracy," former President Obama said in a statement.
Democratic former US Representative Gabby Giffords, who was critically wounded by a gunman in 2012, said, "Democratic societies will always have political disagreements, but we must never allow America to become a country that confronts those disagreements with violence."
A Reuters/Ipsos poll conducted in October of last year asked if Americans agreed with a statement that it was "acceptable for a member of my political party to threaten and/or intimidate others to achieve a political goal." Just 6 per cent of respondents - a trivially small share in terms of an opinion survey - said they agreed.
