"The lunch you refer to has always been called a festive lunch.
"Arms works hard to include peoples from all faiths to work together in peace and diversity," Dame Susan said.
"Arms uses language that will encompass and include everyone; it is not designed to exclude anyone."
Dame Susan wouldn't say if she thought we should use generic terms and greetings rather than refer to Christmas by name.
"New Zealanders don't like being told what to do and we are mature enough to decide how to celebrate our special days in our own ways."
Arms spokeswoman Chinwe Akomah said the agency recognised that not all migrants and ethnic communities celebrate Christmas.
"As an inclusive organisation that respects and welcomes people from all backgrounds and faiths, we use terms such as 'festive', 'happy holidays' and 'seasons greetings'," she said.
"This is not new. We have been doing so for years. This year, for example, we have organised a festive multi-ethnic pot-luck lunch for all migrants and ethnic communities."
The number of Christians in New Zealand has been declining, from 55.6 per cent of the population in 2006 to 48.9 per cent in 2013.
However, AUT Professor of Diversity Edwina Pio said expunging Christmas by New Zealand organisations "is a bridge too far".
"I would strongly urge organisations to display their respect, not by erasing the word Christmas, but by being more inclusive so that they keep Happy Christmas, but then also remember to wish individuals for Diwali, Eid Mubarak, Buddha Purnima, Happy Hanukkah and other faith-based festivals," she said.
"I think New Zealand often bends over backwards in their aim not to offend minorities in terms of terminology.
"Erasure does not mean equality. In fact, erasure does not show respect for the heterogeneity that is New Zealand."
The Anglican Dean of Auckland, the Very Rev Jo Kelly-Moore, said people should be looking into the real message the Christmas greeting brings, "one of peace, hope, love and joy" in these troubled times.