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Carr's dark, often inappropriate humour is his trademark style, but many social media users are suggesting he's gone too far this time.
The tweet in question features four images of a puppet version of Carr, in front of four sights of Dunedin.
Carr's caption read, "Went to Napier, destroyed by an earthquake - rebuilt - beautiful town. Went to Christchurch, destroyed by an earthquake - rebuilt - beautiful town. I'm now in Dunedin.
"I'll tell you what this town needs..."
Carr's audience was split on their opinion of the gag.
Some blasted the comedian for being insensitive, labelling the joke as "not okay" and "a bit harsh".
"Earthquakes are hilarious aren't they..." one user posted.
"Aww come on man, people like your gags sailing close to the wind but don't be a f**kwit with it," another said.
"Dude, waaaay too soon. Some of us survived those quakes. Too many of us didn't. Don't joke about tragedies, especially ones you haven't experienced," another complained.
Other dedicated fans came out in support of Carr, calling the joke a "great gag" and "hilarious".
"Lol hilarious. TRUE! Dunedin needs a quake or a bomb. Maybe both. Let's bring Dunedin into the 2000s finally," one brave Tweeter posted.
Another camp of Tweeters took issue with Carr's decisive statement that Christchurch had been rebuilt.
"Just so you know, I live in Christchurch and it's not rebuilt, far from it. It is taking way too long," one person said.
Carr was travelling New Zealand as part of his world tour, hitting stages in Auckland, Hamilton and New Plymouth amongst others.
The questionable gag wasn't his first earthquake-related joke he'd posted to Twitter, having made a jibe about Napier and Christchurch being part of the "earthquake tour" just over the weekend.
Again, this first joke was shot down by users calling it "poor taste" and "offensive".