Watch: Prime Minister Christopher Luxon speaks after formal swearing-in ceremony in Wellington

Prime Minister Christopher Luxon is speaking after the formal ceremony in Wellington to swear in the new coalition government.

Luxon signed separate coalition agreements with ACT leader David Seymour and New Zealand First leader Winston Peters in Wellington on Friday.

Peters will be Deputy Prime Minister for the first half of the parliamentary term, with David Seymour taking over for the remainder.

Cabinet will have 20 members; 14 National ministers, three ACT ministers and three New Zealand First ministers.

Luxon said the government's "number one job" was to fix the economy.

"We actually have to reduce the cost of living, get inflation under control so we can lower the interest rates, we can make food more affordable, we can deal with lower rents, lower fuel.

"A lot of our focus is on tackling the underlying causes of inflation and that does mean a series of things, of making sure that we're generating savings out of the public service and public spending is being prudent, but equally, making sure we do things like get the Reserve Bank focused on a single target."

He said in addition to getting inflation under control, the government would be focused on "restoring law and order, and making sure we deliver, ultimately, better public services".

Asked if he had felt the weight of the responsibility at today's swearing-in ceremony, Luxon said: "I really enjoyed today."

"It is genuinely an awesome responsibility and so I think the ceremony is incredibly weighty that actually every minister understands the responsibility that they have."

"As I said, it is a really special privilege to do public service, that's why we genuinely leave what we're doing and actually come to this place, to try and advance the lives of all Kiwis, and that's what we've gotta do as a government."

Asked how he reconciled the amount of te reo Māori heard in the ceremony with the government's direction, Luxon said he encouraged people to use more te reo.

But he said he wanted people to be able to navigate their government.

"We've had a public service that actually has had more people added to it, more spending taking place, worse results, and one of the things is we need every New Zealander to understand what those agencies are and what the services they provide are."

Luxon said he wanted to be driving programmes that are advancing Pacific people in New Zealand.

"But we want to make sure we're putting money behind good programmes that are actually achieving results, and that's not peculiar just to the Pacific People's Ministry, that is actually our approach to the whole of public service."

On the smoking legislation; asked if it was disingenuous to use that to pay for tax cuts when it was not something they campaigned on, he said he would not characterise it that way.

"Essentially, the government passed some legislation before the election that hasn't really taken effect in the country."

He said the coalition parties did not believe that "some of those component parts" of that legislation was the best way to lower smoking in the country.

Asked if all the 'dollars and cents' required to deliver the government's promised tax cuts would be laid out in the upcoming mini-Budget, Luxon said: "We need to get back to the office and we need to get briefed by Treasury and actually understand the state of New Zealand's fiscal position. We are concerned and worried about that, it's been a deteriorating picture for a number of months now".

"We also are concerned that the Labour government has left us some fiscal cliffs and some fiscal holes and so until we get our head around all of that ... yes, we'll have a mini-Budget, but we'll take any actions or decisions that we can in order to try and improve the situation."

He said it was likely the Treaty Principles Bill would be introduced to Parliament after Christmas.

In response to a question about whether having such a large executive was hypocritical, given his party had campaigned on cutting the public service, he said he did not think it was.

Luxon said the executive was not "excessively large" but it was an acknowledgement that there were three coalition partners.

"We need to go to work and we need to make sure we've got the right people on the right assignments and we've thought very deeply about who's best to lead that work."

Deputy Prime Minister Winston Peters said race relations would improve.

"They'll strengthen based on a thing called equality; they'll be based on the very thing that was said by somebody who knew a bit more about it than you ... the name was Whina Cooper, she said in 1990, that we signed the Treaty so that we could have a country where everybody was equal. One citizens - one group of people in that sense."

Asked what his first trip was likely to be (as minister of foreign affairs) and whether he would likely be focusing first on the Pacific, Peters said: "That's a good question but I'm having a serious briefing this afternoon to be brought up to date on everything ... so I can't answer that question".

Asked if he might go with Luxon to Australia, he said: "I don't know; in this coalition we tend to consult before we do anything rash like a mad commitment like that. Possibly, we'll see what he thinks."

ACT Party leader David Seymour, asked what the minister of regulation role entailed, said: "Two things; first of all to make sure that the assessment of the quality of new laws is high - we don't want laws where we don't know what problem we're solving, the benefits don't outweigh the cost, or it's not clear who the winners and losers or whether there was a better way to do it - so we're going to have very high quality of regulatory impacts analysis for major regulatory initiatives.

"We're also going to start looking through the regulations and laws that have built up in each sector ... look at what rules maybe don't make sense anymore and create an omnibus bill that will delete nonsensical rules so that it's easier for people to spend more time being productive and less time actually ... compliance [SIC] with rules that don't make sense."

Asked if a charter school would be open by term one of 2024, Seymour said it would not be.

There was a process required which would take "at least a year", he said. "So potentially in term one, 2025, but not in the next three or four months."

Asked how some of New Zealand First's "war on woke" policies sat with a socially liberal party like ACT, Seymour said: "We believe in universal human rights, that it's what you do in life that matters more than who you are or how you're born, and I think you'll find there's a lot of consistency with the direction of this government and those fundamental values".

He said he thought there was a "legitimate debate around gender and sexuality education, who should introduce children to these ideas and at what age. There's not necessarily a right and wrong, or a right and left on a question like that".

He said he had "no problem with the name Te Papa. I think it's a beautiful name that is well known to Kiwis up and down the country, I would be surprised if we had an intention to change that, but you never know, there could be people involved in that area of policy who believe that that needs to be done, in which case, we'd assess the case for it".