Buttigieg on Monday declined to engage with a Trump administration official who accused him of pushing a "hate hoax" during his back-and-forth with Vice President Mike Pence.
The US ambassador to Germany, Richard Grenell, on Monday accused Buttigieg of using the feud to further his presidential candidacy, saying it was "along the lines of Jussie Smollett."
Faced with the words of Grenell, who is also gay, Buttigieg paused and parried.
"I'm not a master fisherman," the South Bend mayor said to applause, "but I know bait when I see it and I'm not gonna take it."
Buttigieg and Pence have sparred in the press over the past couple weeks.
"If me being gay was a choice, it was a choice that was made far, far above my pay grade," Buttigieg said at the LGBTQ Victory Fund National Champagne Brunch in Washington earlier this month. "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."
Pence, during his time as governor of Indiana, signed the Religious Freedom Restoration Act, a controversial bill that effectively allowed businesses to discriminate against gay customers.
In a subsequent interview with CNN, Pence said, "I hope that Pete will offer more to the American people than attacks on my Christian faith or attacks on the President as he seeks the highest office in the land," adding, "he'd do well to reflect on the importance of respecting the freedom of religion of every American."