The threat to the tree sparked a petition signed by Fergusson Park and Waratah St residents who live in the area covered by the covenant.
Mayor Stuart Crosby led the debate in which it was agreed that the council would not apply to the courts to modify the covenant so that the tree might live.
Mr Crosby said while the removal of the tree disturbed him greatly, the council must uphold covenants.
Referring to a 2007 challenge to seven of the bank's pohutukawa, he said the council had reached an arrangement to retain three of the seven trees, at the goodwill of the residents who had the power to enforce the covenant. "But that has changed for whatever reason."
Mr Crosby said it was not appropriate for any landowner to have to go to court to enforce a covenant.
Seeking a modification of the covenant would be a long and expensive process with an unknown outcome.
Councillor Rick Curach said court action costing at least $35,000 would be unreasonable given it was only one tree.
Councillors John Robson and Bev Edlin opposed, with Cr Robson saying the council should be acting in the community's interest.
"If we can't change a previous decision of the council, then I question why we are here."
He said the 2007 decision inferred a trade-off had been reached with Waratah St residents in which four trees would be felled in exchange for three remaining.
Agreeing to this tree being removed was, in effect, agreeing to the rest being felled because they would be vulnerable to requests from residents covered by the covenant.
"I see three trees going because of a lack of clarity around decision-making eight years ago," Mr Robson said.
Mr Crosby said it was clear that what was done in 2007 was an informal agreement and not binding.
He was supported by councillors Matt Cowley, Rick Curach, Bill Grainger, Gail McIntosh, Steve Morris and Catherine Stewart. Absent were Kelvin Clout and Leanne Brown.
Pohutukawa tree timeline
November 2014:
Application received to remove tree
February 11:
Residents notified of intention to fell tree
February 16:
Council receives 92-signature petition opposing removal
March 17:
Council lets the issue lie on the table pending more information