Viewers took particular issue with a clip in which Mr. Wooley, interviewing Ms. Ardern and her partner, Clarke Gayford, suggested there had been speculation about the date Ms. Ardern conceived.
“It’s interesting how people have been counting back to the conception, as it were,” Mr. Wooley said.
Grimacing, Ms. Ardern and Mr. Gayford appeared shocked at the question, before Mr. Wooley said there was “no reason a child shouldn’t be conceived during an election campaign.”
“I should add that the election was done,” said a visibly uncomfortable Ms. Ardern, whose due date is in June. “It was over. Not that we need to get into those details.”
Twitter users were swift to respond, including some who suggested Mr. Wooley would not have asked the same question of another official much in the news lately: the former Australian deputy prime minister, Barnaby Joyce, who is having a child after an affair with a former staff member.
At another point, Mr. Wooley expressed surprise that Mr. Gayford would do the laundry at home. The interview devoted less attention to Ms. Ardern’s policies or her administration’s plans than it did her personal life.
On Monday Ms. Ardern was sanguine about Mr. Wooley’s interviewing style, telling reporters in New Zealand she had been “taken aback, but not offended.”
Mr. Wooley, meanwhile, criticized the backlash, telling a New Zealand radio station, “It’s a bit Orwellian” to have to be so careful what you say.
He said he had enjoyed spending time with Ms. Ardern and Mr. Gayford, who were a “wonderful couple.”
With her youth and unexpected political rise, Ms. Ardern, 37, has captured attention across the world. Some journalists have attributed her ascension to “Jacindamania.”
While much of the media attention has been flattering — including a spread in Vogue this month — Ms. Ardern has faced sexist questions in the past. When she rose to the leadership of the center-left Labour Party ahead of New Zealand’s election last fall, she hit back at a television reporter who asked if she planned to have children, saying it was not appropriate to have to answer that.
Ms. Ardern announced her pregnancy three months after taking office, saying she had found out the same week she learned she would be prime minister. She was credited with reversing the fortunes of the ailing Labour Party with her optimism and enthusiasm, after it had spent nine years in the opposition.
Ms. Ardern is expected to be the only national leader in recent years to give birth while in office. In 1990, Benazir Bhutto had her second child while she was Pakistan’s prime minister.
Ms. Ardern has said that she plans to take six weeks of parental leave and that Mr. Gayford will then take leave.
The host of a television show about fishing, Mr. Gayford made a veiled comment on Monday about the Wooley interview, posting photos of the New Zealand coast on Twitter and suggesting it was a place “to escape for ‘60 Minutes’ or longer, where required.”