(CNN) South Bend, Indiana, Mayor Pete Buttigieg's recent rise in the 2020 presidential race has featured a steady stream of attacks against Vice President Mike Pence, the former Indiana governor who had a working relationship with the mayor during his time as the head of the state.

Pence himself has not responded to the pointed attacks, but on Tuesday, second lady Karen Pence and the vice president's spokesperson pushed back on Buttigieg's critcisms.

"They've always had a great relationship," Karen Pence said on Fox News host Brian Kilmeade's radio show on Tuesday. "It's funny because I don't think the vice president does have a problem with him, but I think it's helping Pete to get some notoriety by saying that about the vice president."

The comment comes after Alyssa Farah, Pence's spokeswoman, tweeted that Pence -- as governor -- responded to the mayor's coming out in 2015 by saying he holds Buttigieg "in the highest personal regard. I see him as a dedicated public servant and a patriot."

Karen Pence responded to that on Tuesday.

"I'm just like, 'Pete, did you not like that,' because that's what the vice president said about him," she said. "So what's the problem with that?"

Buttigieg appeared to respond to the comments from Pence's orbit on Tuesday, tweeting, "People will often be polite to you in person, while advancing policies that harm you and your family. You will be polite to them in turn, but you need not stand for such harms. Instead, you push back, honestly and emphatically. So it goes, in the public square."

Buttigieg, most recently, targeted Pence at a fundraiser for the LGBTQ organization Victory Fund on Sunday.

"If me being gay was a choice, it was a choice that was made far, far above my pay grade," Buttigieg said. "And that's the thing I wish the Mike Pences of the world would understand. That if you got a problem with who I am, your problem is not with me -- your quarrel, sir, is with my creator."

Buttigieg's comments came hours after he made critical comments about evangelical voters' support of President Donald Trump during an appearance on "Meet The Press."

"It's something that really frustrates me because the hypocrisy is unbelievable," Buttigieg said. "Here you have somebody who not only acts in a way that is not consistent with anything that I hear in scripture in church."

Update: This story has been updated to note that Vice President Mike Pence has not directly responded to Buttigieg's criticisms.