New Zealand prime minister Jacinda Ardern has given birth to a daughter and posted a photo welcoming the healthy newborn “to our village”.

She is only the second elected world leader to give birth while holding office after late Pakistan prime minister Benazir Bhutto had daughter Bakhtawar in 1990.

Ms Ardern posted a photo on her Instagram account showing her and partner Clarke Gayford with the baby at Auckland City Hospital. The girl arrived at 4.45pm weighing 7.3lb.

“Welcome to our village wee one,” She wrote in the photo caption. “Feeling very lucky to have a healthy baby girl.”

She thanked everyone for their kindness and wishes. “We’re all doing really well,” she wrote.

The pregnancy was followed around the world, with many hoping the 37-year-old would become a role model for combining motherhood with political leadership.

Former prime minister Helen Clark said it was a happy day for Ms Ardern and Mr Gayford and New Zealanders had taken the news of the pregnancy in their stride.

“This is a sign of our maturity as a country and its acceptance that combining career and family is a choice which women are free to make,” she wrote.

“Let’s also celebrate Clarke as a modern man who is happy to be the full-time parent of a young child.”

“For New Zealand, these events and the way our country has greeted them will be seen as inspirational by all who advocate for gender equality and women’s empowerment,” Ms Clark said.

Jennifer Curtin, a professor of politics at the University of Auckland, said there was symbolic importance in Ms Ardern giving birth as it showed political parties around the world that it was fine to have younger women as candidates.

She said women often tended to be older when they entered politics. In other fields, women have been combining motherhood and paid work for decades, but it has only recently become more manageable thanks to paid parental leave.

Deputy prime minister Winston Peters has taken over as acting PM. Ms Ardern plans to take six weeks of leave before returning to work.

Under the arrangement, she will still be consulted on major decisions, including issues of national security. She has said she is confident the government will continue to run smoothly in her absence.

She said that after the birth, she hoped to have some quiet time to enjoy as a family.

Asked earlier this month how the couple had been faring in their quest to choose a baby name, Ms Ardern responded: “Terribly. Do you have any suggestions?”