Scott Robertson and Sam Whitelock feel it is more important to give people time to grieve than rush into a decision over a potential name change for the Crusaders following the Christchurch terror attacks.
Fifty people were shot dead and dozens more were injured in massacres in two mosques last Friday.
Crusaders stated that they would discuss changing the name of the Christchurch-based franchise, but stressed that the name is a reflection of the "crusading spirit of this community" rather than a religious statement.
New Zealand sports minister Grant Robertson stated on Tuesday that it is "appropriate" to enter dialogue over a new name for the Super Rugby champions.
Head coach Robertson says Crusaders will support whatever decision is made, but that should not be a priority for the time being.
He said in a video posted on the club's Facebook page: "We're a rugby club, that's what we do, we play rugby.
"The association of the name, we want to go through a process, we want to let people grieve, we want to make sure they've got time, and we'll go to the people that can represent them and get the information we need to make a great decision and do the right thing."
Crusaders and All Blacks lock Whitelock said: "I think at the moment this is much bigger than rugby.
"We are just trying to make sure we take the appropriate time and make sure we are respectful and those decisions will happen in time.
"But at the moment we are just trying to give everyone space where they need it and those things will happen in the future when it is most appropriate."
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