Three people, including the gunman, were dead and six others were injured in a "serious" gun incident in Auckland, a city in New Zealand's North Island, Prime Minister Chris Hipkins said on Thursday.

The injured, who have been taken to the Auckland Hospital, included a member of the police, Hipkins added.

The assessment from officials is that there is no national security risk and there is no change to New Zealand's security threat level, the Prime Minister told the media.

The offender was armed with a pump action shotgun. He moved through a building site and discharged his firearm, Hipkins said as quoted by Xinhua news agency report.

"Upon reaching the upper levels of the building, the man contained himself in an elevator and police engaged with him, shots were fired and he was located a short time later," the Prime Minister added.

Eight gunshots were heard, according to witnesses.

Connecting streets have been cordoned off, and the public was asked to stay indoors.

Auckland Mayor Wayne Brown said all FIFA personnel and international football teams were safe.

Thursday marked the beginning of the month-long FIFA Women's World Cup 2023, which is being co-hosted by New Zealand and Australia. 

New Zealand women's national football team will face Norway at the opening match at Auckland's Eden Park later on Thursday.