Some Republicans have promoted a version of the "replacement theory" that motivated the Buffalo shooter.
Insider and 2 other reporters repeatedly asked McConnell about the theory, but he wouldn't denounce it.
He said racism "ought to be stood up to by everybody, both Republicans and Democrats."
Facing repeated questions from Insider and other reporters about his party's association with the so-called replacement theory, Senate Minority Leader Mitch McConnell repeatedly declined to condemn it at his weekly press conference at the Capitol on Tuesday.
"This horrible episode in Buffalo is a result of a completely deranged young man who ought to suffer as severe as possible penalty under the law," he said when asked whether he has the responsibility to speak out on the theory as a Republican leader.
"Racism of any sort is abhorrent in America, it ought to be stood up to by everybody, both Republicans and Democrats, all Americans," McConnell said when pressed further.
Insider then asked McConnell whether he believes Democrats are seeking amnesty for undocumented immigrants for the purpose of influencing and changing the electorate and giving themselves a political advantage - a version of the theory promoted by right-wing media outlets and some Republican politicians.
But he demurred a third time.
"What I'm concerned about with regard to the southern border is the relative openness of it," he said, criticizing the Biden administration for lifting Title 42.
On Saturday, 18-year-old white man Payton Gendron opened fire at a Tops supermarket in a predominantly Black area of Buffalo, New York, killing 10 people and wounding several others. Gendron is an avowed white nationalist and an adherent of replacement theory, according to a 180-page manifesto and a compilation of messages written online by someone who identified as Gendron.
In the wake of the shooting, Republicans and right-wing media have come under greater scrutiny for promoting watered-down versions of the theory, which posits that white people are being replaced by people of color and that the "white race" faces demographic and cultural extinction.
Versions of the theory have been promoted on right-wing outlets like Fox News and by Republican members of Congress, most notably House Republican Conference Chair Rep. Elise Stefanik of New York. Generally, arguments about replacement theory are framed in terms of voter power, with Republicans arguing that Democrats want to use immigration to dilute Republican votes.
"Radical Democrats are planning their most aggressive move yet: a PERMANENT ELECTION INSURRECTION," a September ad from Stefanik read. "Their plan to grant amnesty to 11 MILLION illegal immigrants will overthrow our current electorate and create a permanent liberal majority in Washington."
President Joe Biden condemned "those who spread the lie for power, political game and for profit" at an event in Buffalo on Tuesday, though he declined to name any particular person or identity.
But congressional Democrats have gone further, with Senate Majority Leader Chuck Schumer slamming Fox News and Tucker Carlson for spreading the idea, while House Democratic leadership condemned Stefanik by name.