On Saturday, a rally was held in Hagley Park and was followed by a march down Riccarton Rd.
Tamaki reportedly spoke at the event, in a possible breach of his bail conditions, though a Destiny spokesman told NZME the event was a "family picnic", not a protest.
Under orange restrictions, any event held without vaccine pass requirements is limited to 50 people. However, photos and videos posted to social media show more than 100 people attended the outdoor event.
In a statement, Canterbury district commander Superintendent John Price said Saturday's protest action is being investigated.
"Police are looking into whether there are any breaches with regard to Saturday's protest action in Christchurch, following which enforcement action may be taken," he said.
"We encourage individuals attending protests to conduct themselves in a safe manner and adhere to current Covid-19 orange restrictions, which are there to ensure the safety of all."
Tamaki told Stuff he did not organise the event and was invited to speak because he was in the city to preach at the Destiny Church service in Cranmer Square on Sunday.
"As I move around the country to visit our churches I should not be subjected to media lynchings when I am doing my best to adhere to current Covid rules.
"I also should not be an unfair target by NZ Police when they have an obligation to apply the current Covid laws in a fair and consistent manner, which clearly has not been the case to date when it comes to myself, and then they show leniency towards others."
Destiny Church Christchurch Senior Pastor Derek Tait told NZME Tamaki didn't attend a protest, but rather a family picnic
Tamaki, 63, has been charged three times after speaking at large protests in alleged breach of Auckland's lockdown rules. Last month he was again released on bail after a third protest against Covid-19 vaccine mandates at Auckland Domain.
Tamaki has pleaded not guilty to all of the charges, including allegations he violated the conditions of his bail.
After Tamaki's most recent arrest on November 23, Auckland District Court Judge Steve Bonnar agreed to alter Tamaki's bail conditions further to explicitly bar him from Auckland Domain. The judge also altered an existing condition to make it clear Tamaki is barred from speaking at gatherings deemed unlawful.
In late December, High Court Justice Geoffrey Venning agreed to the slight tweak to Tamaki's bail conditions after his lawyer appealed against the restrictions at a hearing.
Tamaki can now visit Auckland Domain for recreation or to visit Auckland Museum.
But he cannot be at the domain on any day that a protest against the Covid-19 Public Health Response Act is advertised or taking place, Venning determined.
Tamaki, whose previous bail conditions include not attending or organising any protest and not accessing the internet for the purpose of organising or inciting non-compliance with Covid-19 level requirements, is scheduled to next appear at the Auckland District Court on April 1.
His wife Hannah Tamaki is also set to make her first court appearance on April 1 - charged with two counts of failing to comply with a Covid-19 order.
