Little Aayushi Deswal will grow up with a special story she can tell on her birthday.

She was born at Auckland City Hospital, on Thursday, just down the corridor from where Prime Minister Jacinda Ardern was making history as the second woman to give birth while in the position of leading a country.

Aayushi's mother Sucheta Deswal was thrilled that her daughter shares a birthday with the daughter of the Prime Minister.

"It's crazy to think we were in the same hospital. We are really happy for her, it's awesome and so special," she said.

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When Deswal discovered she had the same due date as Ardern - June 17 - she realised there would be a chance the two would cross paths in hospital.

"I thought, there is a slight chance we will have the babies on the same day but didn't really think about it too much," Deswal said.

"But then I was a bit delayed obviously and it just so happened that Jacinda was a bit delayed as well, meaning we had our babies on the same day after all."

The two women were in labour almost 12 hours apart. Aayushi arrived just after 6am on Thursday when Ardern had only just been admitted to hospital. The Prime Minister gave birth 11 hours later at 4.45pm

Father Arun Deswal said there was a bit of chatter and speculation at the hospital that Ardern was there.

"Then when we were checking out of the hospital there were quite a few security guards sort of hovering around and our midwife whispered to us, 'I think Jacinda is going to be here', but it wasn't confirmed at the time, no one was saying anything," Arun said.

Deswal moved to Birthcare in Parnell, where she was discharged at 2pm yesterday.

Ardern and Gayford are yet to name their baby but the Deswals named their girl Aayushi, which is a traditional Indian name meaning "long life".

Born on June 21, the baby girls will share their birthday with Prince William, Indonesia's President Joko Widodo, singer Lana Del Ray and NSA whistleblower Edward Snowden.

They also share a birthday with former Pakistan Prime Minister and first female leader of a Muslim nation Benazir Bhutto.

In 1990, Bhutto was the first head of government to give birth while in office.