WELLINGTON, New Zealand — Jacinda Ardern, New Zealand’s prime minister, shared the debut of a new assistance package for families from her couch in a Facebook Live video in which she could be seen cradling her 10-day-old daughter, Neve, in a bundle of blankets.

Between parenting jokes and policy explanations, she called the $5 billion package of tax cuts and payments “the most significant change to the country’s welfare system in decades.” Of all her government’s efforts, “this is the thing I’m most proud of,” she said, telling the audience that if she looked tired it was only because she was not wearing makeup.

The video from July was just one example of Ms. Ardern testing the reach of what she describes as politics “with a bit of heart.”

In many ways — temperament, style and policy, among them — Ms. Ardern is the polar opposite of President Trump and other brash male leaders.