"I'm aware of the conversations that they're now having with - in particular - the Muslim community in Christchurch," Robertson said.
"I think that's appropriate, clearly this is a big issue in Canterbury.
"The Crusaders is a well-established name and brand, but I think it's a responsible action to undertake those conversations now."
The minister didn't, however, feel comfortable expressing an opinion on the matter just yet, saying it was important that discussions were held between the team and the wider community first.
"I'm not going to express opinion on that today," he said. "It's more important that conversation happens with the Muslim community in Christchurch, and the wider Canterbury community. Then I'll take some soundings after that."
On Sunday night, the Crusaders issued a statement saying they "understood the concerns that have been raised" and will consider changing their name.
"For us, the Crusaders name is a reflection of the crusading spirit of this community," the statement read. "What we stand for is the opposite of what happened in Christchurch on Friday; our crusade is one for peace, unity, inclusiveness and community spirit.
"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 is not right now."