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A gunman opened fire at a building site in central Auckland on Thursday in an "alarming incident" that left two people and the shooter dead, New Zealand police said.

The shooting, which also wounded multiple people, coincided with the opening day of the Women's World Cup co-hosted by New Zealand and Australia.

New Zealand Prime Minister Chris Hipkins said there was no national security threat and the tournament would proceed as planned.

The US national team, currently staying in Auckland, said in a statement that all its players and staff were accounted for and safe.

"The offender has moved through the building site and continued to discharge his firearm," police acting superintendent Sunny Patel said.

"Upon reaching the upper levels of the building, the male has contained himself within the elevator shaft and our staff have attempted to engage with him," he added.

"Further shots were fired from the male and he was located deceased a short time later."

Police said two deaths had been confirmed so far, in addition to the attacker. They also reported multiple injuries.

Officers responded in "significant" numbers to the morning shooting and cordoned off the area, police said, also deploying a helicopter.

Details are still emerging, Patel said.

"What has unfolded is understandably alarming and we are reassuring the public that this incident has been contained and is an isolated incident," the officer said.

"We can also advise that this is not a national security risk."

Police asked people to stay away while they investigated the emergency.