Former New Zealand Prime Minister Helen Clark believed Ardern and Gayford had sent a significant message to the world, particularly with Gayford being a stay-at-home dad.
The realities of motherhood have seen plans for a public appearance by the 37-year-old with her baby cancelled twice.
Ardern's Australian counterpart Malcolm Turnbull told ABC Radio he was "really thrilled", while New Zealand opposition leader Simon Bridges offered congratulations.
Ms Ardern's office said the shawl wrapped around her daughter in the photograph on her social media post was knitted by Clarke Gayford's mother.
The charismatic Ardern follows Pakistan's prime minister Benazir Bhutto in 1990 as the only women in modern history to give birth while in power, but she downplayed the significance.
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Red Bull's Max Verstappen qualified fourth with Australian team mate Daniel Ricciardo fifth and Ferrari's Kimi Raikkonen sixth. I trust the team, and if we have to use the older-specification engine, I am not anxious ".
Jacinda Ardern's newborn daughter is keeping warm in woollies made specially for her, including a baby blanket gifted by Ngai Tahu.
The American ambassador to New Zealand, Scott Brown, on Thursday congratulated Ardern both in English and in Maori, New Zealand's indigenous language.
It said everyone is happy and doing well, if not a bit exhausted.
"The nurses described the baby as 'very alert and one hungry baby, ' " the spokesman added.
She was one of 24 children born at the hospital - the country's largest public facility - on Thursday.
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Trans Day of Action is organised by The Audre Lorde Project - a LGBTQI and people of colour community organisation centre in NY . In March of this year, Nixon announced she would be running for governor of NY against Democrat , Andrew Cuomo .
Ms Ardern moved from the birthing suite on the ninth floor of the hospital to the maternity ward on the 10th floor at 8pm last night. She'd earlier said the quest to come up with a name had been going "terribly".
In a recent interview, Ms Ardern said she was bracing for life in a media bubble for her family.
Ardern found out she was pregnant on October 13, just six days before she was propelled into the job when Peters, the leader of the New Zealand First Party, announced he was siding with her Labour Party in post-election negotiations.
Her plans for a family had sparked a sexism row during the election when a television host quizzed her on the issue, saying voters had a right to know before they cast their ballots.
"As long as the judgement falls on me more than my child, that's what I hope for the most".
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Martínez added: "It was a knock that he had late in the first half and he tried to play through it and he couldn't". Belgium will assess the fitness of all three players within the next 48 hours.
Meanwhile Gayford, in committing to be a stay at home father after Ardern finishes up her six weeks parental leave, is also shattering assumptions and offering a much-needed high-profile reminder that men can take on this role.