On Friday evening, Mr Kemp tweeted a photo of him and his daughter Lucy at the White House Christmas party, standing between elaborate festive decorations.
“Lucy and I had a great time at the @WhiteHouse Christmas Party today. Merry Christmas, everyone!” the governor wrote.
Jenna Ellis, who has led the Trump campaign’s so far fruitless attempts to overturn 3 November’s election results alongside Rudy Giuliani, replied to his tweet, writing: “Seriously?”
The Hill reported that other supporters of President Trump replied to Mr Kemp’s tweet, criticising him for failing to look into the US president’s baseless claims of voter fraud.
President Trump has publicly criticised Mr Kemp and secretary of state Brad Raffensperger in recent weeks, after he became the first Republican to lose the state in nearly 30 years when he lost to President-elect Joe Biden on 3 November.
Speaking to Fox News in November, President Trump said that he is “ashamed” that he endorsed Mr Kemp for governor in 2018, after claiming that he had “done absolutely nothing” to question the state’s results.
The following day, Mr Trump described Mr Kemp as “hapless” and said he should use his “emergency powers, which can be easily done, to overrule his obstinate Secretary of State,” in reference to Mr Raffensperger.
Mr Kemp has tried to keep out of the public feud, with runoff races in the state scheduled in January to decide which party has control of the US Senate, but his spokesperson said that Georgia law bars him “from interfering in elections.”
Although Mr Biden was declared the winner of the presidential election last month, Mr Trump has repeatedly falsely claimed that there was widespread voter fraud and has still not conceded.
Mr Trump and his team have had more than 50 legal challenges dismissed over the last month, including in Georgia, as he and his allies are still attempting to overturn 3 November’s election results. There is no evidence for the claims.
The governor posted the photo at the White House party on Friday just hours after President Trump had once again criticised him and Mr Raffensperger, calling them “so-called ‘Republicans.”
President Trump also criticised Mr Kemp earlier in the week, when he retweeted a post from a conservative attorney that called for him and Mr Raffensperger to be jailed.
On Tuesday, Mr Trump retweeted a tweet from Lin Wood, an attorney who has filed multiple unsuccessful lawsuits in an effort to help the president overturn 3 November’s election results.
“President Trump…is a genuinely good man. He does not really like to fire people. I bet he dislikes putting people in jail, especially ‘Republicans,’” Mr Wood said.
“He gave @BrianKempGA & @GaSecofState every chance to get it right. They refused. They will soon be going to jail,” he added, in the post that was retweeted by President Trump on Tuesday morning. Neither official or the White House responded to the tweet.
On Friday, The New York Times reported that President Trump cancelled a planned visit to Georgia this weekend, to help campaign for Republican senators Kelly Loeffler and David Perdue, ahead of the runoff elections.
A senior Republican official told the Times that the trip was cancelled, because of the president’s continued anger with Mr Kemp and Mr Raffensperger.