Mr Kinzinger tweeted that Mr Gaetz was “wrong, by like a huuuuuuge margin” for claiming there were enough votes to ouster Ms Cheney, ahead of the first attempt by Trump allies.
The Florida congressman also falsely alleged that “the establishment” would overturn the results of the first vote, in February.
With wider support for Ms Cheney’s removal ahead of Wednesday’s vote, Mr Gaetz resurfaced the tweet by the Illinois congressman and wrote: “Tweets that don’t age well”.
Mr Kinzinger fired back by tweeting at Mr Gaetz – who is facing a federal investigation for allegations of sexual trafficking – “I’d stay away from ‘ageing well’ tweets.” Mr Gaetz denies the allegations.
The back-and-fourth follows a fracturing of the Republican party in Congress, and frequent criticism of the former president for lying about election fraud by Mr Kinzinger and the conference chair.
Ms Cheney, the daughter of former Republican vice president Dick Cheney, told Congress on her stance on the former president that “remaining silent and ignoring the lie emboldens the liar”, in reference to Mr Trump.
Elise Stefanik, a Trump ally, is favoured to replace Ms Cheney after receiving endorsements from the former president and Republican minority leader Kevin McCarthy – who in February stood with Ms Cheney.
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