Police said the man was wearing a "Trump" t-shirt and black cap and had "shaken" the Muslim community late Wednesday at the Al Noor mosque by shouting abuse at people.
"Our community has no tolerance for those who target or victimise others because of their identity, and nor does police," Canterbury district commander superintendent John Price said in a statement Wednesday.
"This is especially so for members of our Muslim community who are already dealing with so much," he added.
The man walked off into the park opposite the mosque after the incident. Police renewed their calls Thursday, seeking to identify the man they described as "of solid build with short dark hair and a tattoo on his left shoulder/neck area".
Police said they are reviewing their response as two armed officers were at the mosque at the time of the incident.
Australian Brenton Tarrant, 28, a self-avowed white supremacist, has been charged with 50 counts of murder and 39 of attempted murder over the Christchurch twin mosque attacks.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)