Buttigieg and his husband are off "trying to figure out how to breastfeed," said Carlson.
Pete Buttigieg has fired back at Tucker Carlson's criticism of his paternity leave.
The 39-year-old Transportation Secretary as been on paid leave since August, when he and husband Chasten welcomed twins Penelope Rose and Joseph August — much to some peoples' irritation.
"Pete Buttigieg has been on leave from his job since August after adopting a child. Paternity leave, they call it, trying to figure out how to breastfeed. No word on how that went," Carlson said on his show on Thursday.
Speaking to Jake Tapper on CNN Sunday night, the new father wasn't impressed.
"As you might imagine, we're bottle feeding and doing it at all hours of the day and night," he said. "I'm not going to apologize to Tucker Carlson or anyone else for taking care of my premature newborn infant twins."
He continued: "The work that we are doing is joyful, fulfilling, wonderful work, it's important work — and it's work that every American ought to be able to do when they welcome a new child into their family."
Buttigieg on Tucker Carlson mocking him for taking paternity leave: "I'm not going to apologize to Tucker Carlson or anyone else for taking care of my premature newborn twins ... it's work that every American ought to be able to do when they welcome a new child into their family" pic.twitter.com/QXUxU1T0Me
Paid family leave was something he said both he and President Joe Biden campaigned on, as he pointed out America was "pretty much the only country left that doesn't have some kind of national policy for paid leave."
"I think it's down to us and Papua New Guinea," he said. "It is long past time to make it possible for every American mother — and father — to take care of their children when a new child arrives in the family."
Buttigieg's critics are unhappy with the timing of the leave, as the US faces a supply chain crisis in the run up to Christmas, with many parents worried about the resulting increase on costs and lack of availability.
Buttigieg warned elsewhere in the interview that the problem may well continue into next year, although he insisted Christmas 2021 was going to look a lot better than 2020's.
"Certainly a lot of the challenges that we've been experiencing this year will continue into next year," he said. "Look, part of what is happening isn't just the supply side, it's the demand side. Demand is off the charts. Retail sales are through the roof."
"And if you think about those images of ships, for example, waiting at anchor on the West Coast – every one of those ships is full of record amounts of goods that Americans are buying because demand is up because income is up because the president has successfully guided this economy out of the teeth of a terrifying recession."
He added: "Our supply chains can't keep up. And of course, our supply chains, that’s a complicated system that is mostly in private hands, and rightly so. Our role is to be an honest broker, bring together all of the different the players there, secure commitments and get solutions that are going to make it easier."