New government speeches coloured by Winston Peters' off the cuff remarks

Things will get better, government spending will be curbed, and there is trust and respect amongst the government parties - the coalition leaders have stressed.

But New Zealand First leader Winston Peters was going off script in the very first collective appearance since the coalition deal was signed.

The leaders of National, ACT and NZ First revealed the details of their coalition agreement Friday, following three weeks of secret negotiations.

Watch the new government speak here:

NZ First leader Winston Peters was the first of the deputy prime ministers to speak.

He quickly took aim at journalists in the room.

"We went to the wire for our people, in the same way that David Seymour did for his, and Mr Luxon did for his as well, and that's the nature of these coalition talks.

"Please understand it was under three weeks, please do not be mathematical morons and keep saying it was 40 days."

As he got into a verbal sparring: "Don't argue about it, it's not a competition.

"You want to argue with me, you should have been there before the election, maybe I'd have got more votes."

Luxon jumped in with "alright, alright".

Back on track, Peters said NZ First "know that it is going to be a much much better government".

The coalition agreement spoke for itself and they got "everything... that we wanted", he said.

"We're back," he crowed as David Seymour was introduced.

The ACT leader spoke for longer than Peters.

He said they wanted to ensure it was a government of real change.

"I believe that we have made a positive and substantial contribution to this government's agenda."

Seymour went on to list ACT's achievements including gun reform, charter schools and the return of over the counter pseudoephderin - "a return to common sense and also great relief".

"There will be wholesale reform of the government's approach of applying social services. We will no longer be treating people differently based on ethnicity as a starting point. We will be focusing public services on need."

He said they would "grasp the opportunity" to make the country better.

The incoming Prime Minister speaks

Luxon book-ended the speeches, declaring it a "historic" occasion and the first time all three parties in a coalition had been represented in Cabinet.

Early on in his speech he thanked Chris Hipkins for his efforts as a caretaker prime minister.

But by end of his comments, he said turning around the "mess" that Labour had left would take time.

"Because it is a big job and we have to get it right."

It wasn't all wins for National - they had to abandon their plan to allow foreign house buyers back in order to fund their tax cuts - but Luxon said ACT and NZ First had agreed to support the "major elements" of National's policies.

"Part of treating taxpayers money with respect is ensuring that New Zealanders get better value from government spending.

"We should all feel confident that the money is being well spent and that for example kids are getting a good education at schools and that the health system is effective and responsive."

He said they would do that by setting targets, like shorter hospital wait-times.

"Whether you are old or young, regardless of your ethnicity, if you live in central Auckland or the deepest south, our government is going to deliver for you."

Luxon outlined which policies had been adopted from each party and covered the key ministerial positions.

Reflections on coalition talks

Each of the leaders had their own take on how the coalition talks had progressed.

Peters called them "seriously long, difficult and complicated talks".

"Arduous in the extreme and we expected nothing less, cause that's the nature of life itself where we are as a country."

But ultimately, they were successful, Peters said.

Seymour said the negotiations were "robust".

"So has the growth in respect amongst us and the reservoir of trust and belief that will allow us to together work through the challenges our country will no doubt face."

He admitted it was a "difficult" process but also "ultimately (a) successful one".

Luxon thanked New Zealanders for their patience saying it was a credit to the country "that we now handle the MMP process with such calmness and maturity".

"The negotiation process has been diligent, it's been focussed and it's been purposeful.

"Our aim has simply been not to form a government but to form a strong and stable government that gets thing done for Kiwis."