It said staff working on the 189-metre suspension bridge on the Hooker Valley Track had repeatedly seen people ignoring safety barriers and gates and were often downing tools to tell people to leave.
On one occasion, staff had to stop a helicopter pouring concrete to tell walkers to go.
Doc Aoraki/Mt Cook operations manager Sally Jones said there were already signs on the track and at White Horse Hill car park warning people not to go past barriers but some people were ignoring them.
"People are taking real risks by climbing fences and in some cases even attempting to cross the Hooker River - it's bloody freezing, let alone fast and furious," she said.
"They're doing this all to get to the closed Hooker Bridge - which is not safe."
"People are putting their lives at risk. We all want the new suspension bridge on the Hooker Track open as soon as possible and the construction workers need to be able to get on with the job without having to worry about the public."
She said as the upper section of the track was a restricted access site, trespass notices could be issued.
"We just want visitors to respect the information we are giving them. Staying on tracks in general is important as our environment can be very challenging and we want people to have a safe trip.
"We sometimes see visitors putting themselves at risk to get that one photo, near a drop-off or way off track. People can also trample over the unique and precious alpine vegetation and don't seem to notice what they are destroying."
Jones said aerial predator control operations were also due to begin in the park, involving temporary closures of Tasman Valley Rd and lower Hooker Track from the first suspension bridge.
"We want to ensure there is minimal disruption to people's plans. There are plenty of other walks in the park which have spectacular views of Aoraki including Kea Point, Sealy Tarns and lovely nature walks like through Bowen Bush and the Governors Bush walk."
