Watch: Christopher Luxon speaks to media after National's election night victory

National Party leader Christopher Luxon says he has spoken to ACT Party leader David Seymour twice and will work with him "in a constructive way", but negotiations had not started yet.

New Zealand voters gave National a mandate to lead the next government with 50 seats in Parliament and just under 39 percent support.

National and ACT together have 61 seats in a 121-seat Parliament, while Labour support fell to just under 27 percent.

The incoming prime minister spoke to media on Sunday morning, after the election night result which gave National and ACT a majority of seats in Parliament.

Luxon said he did speak with ACT Party leader David Seymour twice on Saturday, and would work with him "in a constructive way".

They had also spoken often over the past couple of months - including about rebuilding the economy and law and order which he said they were aligned on - and knew each other fairly well, Luxon said.

"What we've made sure is that we have good alignment and good chemistry and I've done a lot mergers and acquisitions and I've done a lot of negotiations, and getting the chemistry, getting the relationship right is the platform and foundation for then being able to work your way through the transactional issues."

He said he wanted to respect the parties involved and would not be discussing negotiations beforehand via media.

Last night, Luxon wasn't commenting on whether he would offer ACT leader David Seymour the role of deputy prime minister.

Watch the media conference here:

With special votes still to be counted, it was unclear whether Luxon would have to keep the line to New Zealand First open.

Luxon said he hadn't spoken to New Zealand First leader Winston Peters, but appreciated Peters' comments offering to help if needed.

Addressing supporters last night, Peters suggested there were a lot of National's promises that were not affordable and he would work to rein them in, given the chance. "If we can help, going forward, we will," Peters said.

Luxon had not yet spoken with New Zealand First leader Winston Peters yet: "I really appreciated Winston Peters' remarks as I commented last night, on his offer of help and wanting to act in New Zealand's interests and I respect that. I am sure in due course we will be in contact."

The party is back in parliament, with eight projected list seats.

But Luxon reassured New Zealanders: "We will sort it out, we will get a strong stable government, the country voted for change and we have a mandate to form that government with the parties of change."

On ballot voting issues, Luxon said there would be a natural process of looking at what went well and what didn't and any improvements needed.

"I think there was a number of issues where people didn't get their quick vote [EasyVote] cards in place either, there's a number of issues and I think frankly the Electoral Commission has one job which is to get organised every three years for a general election."

He said he was awake until 2am after thanking supporters and spending time with the family, but then stayed awake to review analysis and the full results. "Then it was time to get up and watch the rugby."

He spoke to the Australian prime minister shortly after the conference.

"He's obviously had quite a big event happen yesterday with the Voice referendum and I know that's been a consuming political event in Australia as well ... but rest assured Anthony Albanese and I know each other well from my previous life, we've already met before when he came to New Zealand."

Luxon wanted the relationship with Australia to go "from strength to strength", with it being the number one foreign policy for him.

Albanese posted on X, formerly Twitter, congratulating Luxon and saying he was looking forward to building the relationship between the two countries.

He also thanked Labour leader Chris Hipkins for his term.

National Party campaign chair Chris Bishop said there were still a number of special votes to count for his electorate Hutt South. The margin on Sunday morning was 1094. Labour's Ginny Andersen has not conceded.

Bishop said the big change in the blue wave was in Auckland, where they had picked up a few unexpected seats, including Mt Roskill with Carlos Cheung and Rima Nakhle in Takanini.

"We've also put a real effort in in South Auckland. Siva Kilari in Manurewa, for example, ran an outstanding campaign... We have a put a real effort into Auckland."

Luxon said he was pleased they had stood two candidates in the Māori seats which were about re-establishing a connection.

"We made good progress on our own party votes in the Māori seats as well, whether we had candidates there or no candidates, good results relative to our performance in recent elections, we will continue to build rapport and relationships."

National had a three-part plan consisting of unifying their party in Parliament tackling issues with the Labour-led government on economy, law and order and health and education, and making a case about their priorities, he said.

"This election was always going to be about the economy and that was an issue whether you're a farmer dealing with on-farm inflation and high interest rates or whether you're a mortgagee holder here in Auckland struggling with rapidly increasing interest rates as well, that's what what it was always about and that's what we were very focused on ... we didn't want to bark at every passing car."

He was optimistic about the path going forward but admitted there would be challenging realities to face up to.

He also thanked Labour leader Chris Hipkins, and said being the prime minister was one of the most extreme jobs and he admired anyone who did it to their best ability.

"We might disagree on politics, we might disagree on the way to take the country forward but in New Zealand I want to see civility in our politics - we don't have to go down the pathway we see in other countries around the world."

Luxon said he appreciated he was a new leader and had not come through a traditional political leadership pathway, but he had a range of experience in leadership and that was transferable into politics. He said having people from all walks of life in government was also valuable.