Prime Minister Jacinda Ardern says rates will go up for all New Zealanders if nothing is done about water infrastructure.

Ardern told reporters the focus of her first meeting today with Auckland mayor Wayne Brown was on more housing, better transport options and ensuring rates didn't increase for Aucklanders.

Ardern said she suggested to Brown that key ministers sit down with him once council is finalised.

She reiterated that rates would continue to go up for New Zealanders if nothing was done about water infrastructure.

"I made it clear to the mayor that his speculation about three waters would see rates go up and I am not going to let that happen," said Ardern.

Ardern said increases in rent prices in Auckland were starting to come away.

She said housing intensification in Auckland was important to focus on.

"We still have a housing supply issue."

Ardern also announced that the by-election in Hamilton west will be held on December 10.

"I am still disappointed on behalf of tax payers that we are still having this by-election," she said.

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"It seems to be a complete waste of tax payers money."

The by-election has been triggered by the resignation of Labour MP Guarav Sharma, who fell out with his own party.

Ardern said; "We're having a by-election so that he can come back and do the same job."

She said the Labour party were going through the usual processes when asked if they would be putting up a candidate.

"We will campaign proudly on our record."

Earlier Auckland mayor Wayne Brown described his meeting with Prime Minister Jacinda Ardern this morning as "friendly and constructive" and said it clear that they both shared a goal of making life better for Aucklanders.

The meeting lasted about 40 minutes.

Brown said he raised five major points with the PM: transport alignment, a united front on law and order, updating the Auckland Council legislation, Three Waters and its impact on Auckland and progressing the future of the Ports of Auckland.

"I'm looking forward to working with the Prime Minister and her senior ministers on these important issues facing the people of Auckland," Brown said.

Ardern and Brown met today for the first time today since Brown's emphatic win over Labour's Efeso Collins.

The meeting between the pair was expected to be a polite and friendly, get-to-know-you event, although it was thought both political heavyweights would be measuring one another up for what looks like a bumpy ride for Auckland-Wellington relations.

"I'm certainly going to be polite to her," Brown told Newstalk ZB's Mike Hosking earlier this morning.

"I'm hoping it's very cordial and formal. I'm not quite sure, I'll just sit and listen and see where she takes it, she is the Prime Minister, I have to respect that."

After this morning's meeting with Brown, Ardern will front a media-stand up at 11.10am.

Ardern also met with new Auckland Chamber of Commerce chief executive and former National leader Simon Bridges this morning.

Brown had requested to hold a joint press conference with Ardern after their meeting but this was turned down yesterday.

A spokeswoman for Ardern confirmed there would not be a joint press conference, saying Arden had not held joint press conferences after meeting Wellington's new mayor Tory Whanau and new Christchurch mayor Phil Mauger.

Brown said the call did not disappoint him.

"We just thought maybe the public would quite like to know what we discussed," he said.

On the campaign trail, Brown made no bones about Auckland being bossed about and told what to do by Wellington politicians.

On election day, Brown said: "Let me be very clear: Wellington's job is to listen to what Aucklanders say are our priorities, and to fund them - not impose ideological schemes like the $30 billion airport tram, untrammelled housing intensification and Three Waters on a city that doesn't want them."

He has also talked about using his independence and clout at next year's general elections to see what the parties are prepared to offer up in return for Auckland's support.

For instance, he's thinking of holding an auction on police numbers.

"How many police are you going to give us Labour? 5000, do I hear 6000 from you National. That's the position we are going to be in," Brown said.

Meanwhile, a day after telling transport body Auckland Transport he wants a complete change in its approach, Brown seems bent on making sure that change happens.

Brown told Hosking he was still waiting for a response from AT and that they really did not have much option but to come back to him - eventually.

Put to him that he was the mayor and therefore could be told to "go get stuffed", Brown replied: "Well that's not going to happen, mate. You wait and watch."

It was reported yesterday that the newly elected mayor had sent a written directive to the Auckland Transport acting chairman, Wayne Donnelly, seeking a complete change to the transport body's approach.

"You appear to have been focused on changing how Aucklanders live, using transport policy and services as a tool," Brown said.

"Instead, AT must seek to deeply understand how Aucklanders actually live now, how they want to live in the future, and deliver transport services that support those aspirations."