That daughter, Bakhtawar Bhutto Zardari, congratulated Ms. Ardern on Twitter on Thursday.

In the 28 years since Ms. Zardari’s birth, several women earned their way into their country’s executive mansions and offices, but none spent time in the delivery room while in power.

While news reports at the time of Ms. Bhutto’s delivery said Pakistanis sang and danced in the streets with joy, she also faced criticism for having a second child. Opposition leaders said that “the country would be leaderless while she was hospitalized,” The New York Times reported at the time.

“There is no easygoing ‘mommy track’ for heads of state,” The Times wrote in 1990 about Ms. Bhutto’s uphill political battle.

Ms. Bhutto, who temporarily transferred power to her mother, the lawmaker Nusrat Bhutto, while in labor, announced that she was “back on the job” one day after her delivery.

Years after serving a second term as Pakistan’s prime minister, Ms. Bhutto was assassinated in 2007.

(Trivia buffs might want to note that Ms. Ardern’s baby was born on Ms. Bhutto’s birthday.)

In the United States, several politicians have made headlines for their pregnancies in recent years, including Sarah Palin, who as governor of Alaska delivered a baby in 2008, and Senator Tammy Duckworth of Illinois, whose pregnancy this year prompted the Senate to change its rules about allowing babies and breast-feeding in the chamber.

The American ambassador to New Zealand, Scott Brown, on Thursday congratulated Ms. Ardern both in English and in Maori, New Zealand’s indigenous language. “Tēnā koe i tō tamāhine. Ngā mihi mahana,” he said on Twitter (it means “Congratulations on the arrival of your new daughter, and best wishes”).