“Good people of Georgia, it was never our intention to offend anyone!” the band said in a statement on its Facebook page, adding that it had a longstanding tradition of inviting people to play the drums.
“We recognise that a comment, meant to suggest that all of the Killers’ audience and fans are ‘brothers and sisters’, could be misconstrued,” it added.
The reference was to a remark band leader Brandon Flowers made to the crowd, saying he did not want the situation to turn “angry”.
“I see you as my brothers and my sisters,” Flowers added to the sound of boos and whistles in a video published by the Russian state RIA news agency.
Videos on social media showed people leaving the show, in addition to the booing.
Georgian public opinion is overwhelmingly pro-Ukrainian.
The band has sold millions of albums, with many songs topping the charts since it formed in the city of Las Vegas in the early 2000s.