The latest incident is particularly concerning to WorkSafe which says it has been working actively at the port.
Five improvement notices, six prohibition notices and four written warnings have been issued at the port this year. There are also several ongoing investigations, Mr Murray said.
"On Tuesday, we will talk directly to the port company's senior leadership and worker representatives about the state of affairs at the port," he said.
"There are clearly serious risks at the port that need to be effectively managed and we want to ensure the port company is doing this.
"The face-to-face meeting will be a chance for WorkSafe to set out clearly our expectations of the port, and seek a commitment from the company about how it will respond to the ongoing health and safety issues at the facility."
Maritime Union national secretary Joe Fleetwood said Mr Fletcher's death was a great shock.
"Brad was a highly respected figure in Lyttelton and within the Maritime Union, and the union would be supporting his workmates and family."
The Lyttelton Volunteer Fire Service paid tribute to Mr Fletcher on its Facebook page.
It put up an image of a pair of fireman's boots, with the text reading: "At the end of the day...some of us may never put our shoes back on".
The organisers of the Skytower stair challenge also posted a note about Mr Fletcher.
"Having personally met Brad at Skytower I have to say he was certainly one of the good buggers and is a huge loss to both the fire service and the stair climbing fraternity.
"RIP mate, thoughts and prayers are with your family and your fire service family at station 29."Lyttelton Port of Christchurch chief executive Peter Davie said yesterday the company was "extremely saddened" by the death.
The incident happened at the port's container terminal, he said.
"All staff at LPC are deeply distressed by what has occurred and our thoughts are with the family and friends at this time," Mr Davie said.
"This tragic accident deeply affects everyone in our port community. We are focused on providing support services to the family and colleagues to help wherever possible."
All operations at the container terminal were suspended until today.