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More details are emerging about the timeline of yesterday's construction site shooting in central Auckland.

Armed police were on site in minutes after the shooting began about 7.30am yesterday.

Police Commissioner Andrew Coster has revealed to Mike Hosking members of the Armed Offenders Squad training nearby rushed to the scene, quickly joined by staff from further afield.

\u201cWe had staff response from all over Auckland and we have now quite a good prescence of AOS trained staff on the front line. The staff who went into the building \u2013 and there was quite a number of them \u2013 came from many different working groups.\u201d

The death toll remains at three, including the gunman.

Coster says the conditions of the 10 injured people is improving.

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