The original tweet, which has since been unliked, came from a Twitter account that frequently shares unfounded rumours about the Covid-19 vaccination and encourages anti-government demonstrations around the world.
National leader Christopher Luxon told Newshub he disagreed with the kind of language used by the individual who wrote the tweet.
“That’s utterly unacceptable. I think we need to be very respectful of the reasons the Prime Minister gave for why she resigned and I think we don’t want to put words into her mouth.”
Luxon said he wished Ardern “nothing but the very best”.
Ardern’s bombshell announcement of her resignation on Thursday started a discussion about the insults and abuse directed at her when in power.
Former prime minister Helen Clark said Ardern had faced an unprecedented torrent of “hate and vitriol”.
“I’ve seen the public pressures of vitriol and mouthing against Jacinda in a very, very unfair way and at some point, as she said, you’re human, at some point you don’t have any gas left in the tank, and she’s made the call that is absolutely right for her and her family.”
While Clark faced a huge amount of unpleasant criticism during her nine years as Prime Minister, she told RNZ’s Morning Report that social media had given it more license.
“The amount of anonymous trolling and venomous commentary is absolutely ghastly.
“I was going through the responses to the tweet I put up and the hate brigade is out in force, the anti-vaxxers, the people calling Jacinda a dictator, really just extreme and absurd language.”
Additional reporting from RNZ