Prime Minister Jacinda Ardern burst out laughing on Thursday as she admitted she hadn't "ever had a chat" to Winston Peters about smoking.
And Ardern said she wouldn't negotiate with the New Zealand First leader on his calls for a pack of cigarettes to cost no more than $20.
Peters last week said it was "hypocrisy" holding a cannabis referendum alongside a goal of being smoke-free by 2025.
The Deputy Prime Minister doubled down on those comments on Wednesday and told Magic Talk people were being "screwed" by tobacco tax.
"It's daylight robbery on behalf of successive Governments who say their target is smoke-free by 2025 while the billings they're collecting tell you that they have no genuine plan," he told host Peter Williams.
"The hideous hypocrisy knows no bounds - so you want to know my policy? It wasn't my intention to tell you but I'm telling you right here, right now, $20 should be the maximum for any packet of cigarettes."
When asked by a reporter on Thursday if Labour would reduce tobacco tax, Ardern's response was blunt.
"No," the Prime Minister said. "The leader of New Zealand First has always taken a different view on that but we maintain the perspective that, ultimately, we want people to stop smoking in New Zealand and that [tax] has been one of the tools that, around the world, is used to help reduce smoking," she said.
But Ardern and Finance Minister Grant Robertson, who was speaking to the media with the Prime Minister, were then left humoured by the journalist's follow-up question.
"Have you ever had a chat with him [Peters] about his smoking?" the reporter asked as Robertson chuckled.
"Have I ever had a chat with Winston Peters about his smoking? No," Ardern replied in laughter.
"I really appreciate that you think that would be the case, though."
Peters claimed to have quit smoking in 2017, telling TVNZ at the time, "I realised that my friends in the media were so concerned about my health and fitness that I should take their advice".
The New Zealand First leader was filmed smoking on Otago University's campus earlier this month.
New Zealand has lifted the excise tax on tobacco every year since 2010, raising the cost of cigarettes from about $11 for a pack of 20 to $33 by January 2020. It was put in place in an attempt to deter people from smoking and achieve the Smokefree 2025 goal.
"The Government is determined to reduce the horrendous burden of death and disease caused by smoking," the Ministry of Health says on its website. "The Government has set a long-term goal of reducing smoking prevalence and tobacco availability to minimal levels, thereby making New Zealand essentially a smoke free nation by 2025."