The Crusaders say they will wait before they make any decision about their name.
In light of the Mosque shootings in Christchurch, there have been suggestions that the Super Rugby team should change its name.
The franchise said they'll take on board all concerns.
The Crusaders logo depicts a medieval knight swinging a sword, while horsemen often ride into the Christchurch stadium ahead of matches dressed as medieval knights.
In a statement the franchise says it understands the concerns that have been raised but believes now is not the time to discuss the matter.
"For us, the Crusaders name is a reflection of the crusading spirit of this community. What we stand for is the opposite of what happened in Christchurch on Friday."
While the logo depicts a swordsman reminiscent of the Crusades of the 11th to 13th centuries, the franchise maintains its name reflects the crusading spirit of its community and they stand for the opposite of what happened in Christchurch on Friday.
"In our view, this is a conversation that we should have and we are taking on board all of the feedback that we are receiving, however, we also believe that the time for that is not right now.
"Emotions are very raw and real at the moment. There is the need for this community to wrap our support around those who are most affected by Friday's events, and that is the immediate focus for the Crusaders team. At an appropriate time, we will thoroughly consider the issues that have been raised and our response to that. That will include conversations with a range of people, including our Muslim community.