The port handled 46,673 containers in January, down 4.7 percent on the same month last year. The figure was lower at 4.2 percent on a measure of standard sized containers.
Fifteen cruise ships called in January and 24 are expected in February.
Managing director Jens Madsen said the company was concerned about the economic outlook.
"Over the last few months, there have been reports of significant reductions in container volumes through major world ports such as Singapore and Long Beach.
"New Zealand seems to have remained fairly insulated from the impacts until now."
The port handles 50 percent of all imports and 24 percent of exports by value and overall 35 percent of New Zealand's trade by value.