Jacinda Ardern's newborn 'hungry and alert' with mum 'a bit tired' after staying up all night feeding her

That concludes 1 NEWS NOW's live updates as New Zealand waits for Jacinda Ardern, Clarke Gayford and their baby girl to make their first public appearance.

11.05am: The PMs office has confirmed she recently received a private congratulatory message from the Queen via email on the birth of her baby.

The Prime Minister's Office says it was a private message so it won't be made public.

10.40am: A little bit of info from Auckland City Hospital: the average stay for a first time mother there is 2.3 days.

A billboard in Christchurch congratulating Jacinda Ardern on the birth of her girl. Source: 1 NEWS

10.21am: A large electronic advertising billboard on Moorhouse Ave and Lincoln Rd in Christchurch Central has a message of congratulations for Jacinda and the Baby.

9.55am: The Maori Party has this morning released a statement expressing their "great joy" at the birth of Jacinda Ardern and Clarke Gayford's first child.

"We congratulate Jacinda and Clarke for embracing so publicly a concept that is very much part of a Māori worldview – that children are seen as belonging to, and being the responsibility of the wider whānau and community." Maori Party co-vice-president, Kaapua Smith said.

Google has added this hook to its New Zealand homepage in celebration of the baby. Source: 1 NEWS

9.41am: Google has celebrated Prime Minister Jacinda Ardern's first child with a Google home-page graphic - an interpretation of the original 'fish hook' image from her pregnancy announcement. The illustration is by Stephen Templer, a Wellington based artist.

9.23am: The PM was reportedly up most of last night feeding her baby - who is described as "hungry and alert" by nurses.

Ardern's baby was one of 24 born yesterday at Auckland City Hospital.  

9.14am: Reports from the Auckland City Hospital say Jacinda Ardern  has just woken after a "pretty brief sleep", says 1 NEWS political editor Jessica Mutch.

"Everyone is really well, if not a bit tired," Mutch said.

"Nurses have described the baby as ‘very alert and one hungry baby'.

"After her efforts the PM had a dinner of marmite toast and milo last night."

9.05am: Jacinda Ardern will not appear today publicly outside Auckland City Hospital to front the media.

An update from the Labour Party this morning said she is set to spend another night in hospital.

After Jacinda Ardern gave birth to a healthy baby girl at 4.45pm last night, New Zealanders are today eagerly waiting to hear the Prime Minister speak publicly.

The Labour Party is set to give an update at 9am on whether the Prime Minister will emerge from Auckland City Hospital today to front the media.

Ardern announced a few weeks out from her due date that she would hold a media conference outside hospital following the birth of her first child, before retiring for six weeks maternity leave. 

The newborn weighing 3.31kg arrived at 4.45pm today. Source: 1 NEWS

A key point of speculation is what name name Ardern and Gayford will give their baby girl.

Last night, news of the first baby of New Zealand was revealed on Jacinda Ardern's Instagram.

"Welcome to our village wee one," Ms Ardern wrote.

"Feeling very lucky to have a healthy baby girl that arrived at 4.45pm weighing 3.31kg (7.3lb) Thank you so much for your best wishes and your kindness. We're all doing really well thanks to the wonderful team at Auckland City Hospital."

Ardern now becomes the first elected world leader to take maternity leave - and only the second to have a child while in office - having handed over her duties to her deputy earlier in the day.

The PM's first child is due June 17, and yesterday she released some details around photo ops and hospitals to address public interest. Source: Breakfast

The announcement of the birth spurred celebrations and an immediate outpouring of congratulations on social media and across the political spectrum.

Former prime minister and senior UN official Helen Clark described it as "inspirational", while the leader of the opposition, Simon Bridges, said he was delighted for the new parents.

Meanwhile major media organisations in the United States, Britain, Australia, Europe and Asia launched breaking news banners with the announcement.

Australian Prime Minister Malcolm Turnbull told the ABC he was "really thrilled", while Britain's Labour leader Jeremy Corbyn also sent his congratulations.

British Prime Minister Theresa May retweeted Clarke Gayford's announcement of the birth and added, "Congratulations to @JacindaArdern and @NZClarke on the birth of your little girl."

For her part, Ms Ardern has played down the global attention she's received as a role model in recent months.

"I am able to do what I'm doing because I have enormous support around me and it makes me quite privileged," she said recently.

Determined to keep working until the final moment, Ms Ardern travelled until last week and her office yesterday confirmed she was still texting staff after going into labour to make sure they were fine.